Maximal independent set (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Maximal independent set" in English language version.

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Byskov (2003). For related earlier results see Croitoru (1979) and Eppstein (2003). Byskov, J. M. (2003), "Algorithms for k-colouring and finding maximal independent sets", Proceedings of the Fourteenth Annual ACM-SIAM Symposium on Discrete Algorithms, Soda '03, pp. 456–457, ISBN 9780898715385. Croitoru, C. (1979), "On stables in graphs", Proc. Third Coll. Operations Research, Babeş-Bolyai University, Cluj-Napoca, Romania, pp. 55–60. Eppstein, D. (2003), "Small maximal independent sets and faster exact graph coloring" (PDF), Journal of Graph Algorithms and Applications, 7 (2): 131–140, arXiv:cs.DS/0011009, CiteSeerX 10.1.1.342.4049, doi:10.7155/jgaa.00064.
Eppstein (2003); Byskov (2003). Eppstein, D. (2003), "Small maximal independent sets and faster exact graph coloring" (PDF), Journal of Graph Algorithms and Applications, 7 (2): 131–140, arXiv:cs.DS/0011009, CiteSeerX 10.1.1.342.4049, doi:10.7155/jgaa.00064. Byskov, J. M. (2003), "Algorithms for k-colouring and finding maximal independent sets", Proceedings of the Fourteenth Annual ACM-SIAM Symposium on Discrete Algorithms, Soda '03, pp. 456–457, ISBN 9780898715385.

ams.org

mathscinet.ams.org

Erdős (1966) shows that the number of different sizes of MISs in an $n$ -vertex graph may be as large as $n - log n - O (log log n)$ and is never larger than $n - log n$ . Erdős, P. (1966), "On cliques in graphs", Israel Journal of Mathematics, 4 (4): 233–234, doi:10.1007/BF02771637, MR 0205874, S2CID 121993028.

arxiv.org

Weigt & Hartmann (2001). Weigt, Martin; Hartmann, Alexander K. (2001), "Minimal vertex covers on finite-connectivity random graphs: A hard-sphere lattice-gas picture", Phys. Rev. E, 63 (5): 056127, arXiv:cond-mat/0011446, Bibcode:2001PhRvE..63e6127W, doi:10.1103/PhysRevE.63.056127, PMID 11414981, S2CID 16773685.
Byskov (2003). For related earlier results see Croitoru (1979) and Eppstein (2003). Byskov, J. M. (2003), "Algorithms for k-colouring and finding maximal independent sets", Proceedings of the Fourteenth Annual ACM-SIAM Symposium on Discrete Algorithms, Soda '03, pp. 456–457, ISBN 9780898715385. Croitoru, C. (1979), "On stables in graphs", Proc. Third Coll. Operations Research, Babeş-Bolyai University, Cluj-Napoca, Romania, pp. 55–60. Eppstein, D. (2003), "Small maximal independent sets and faster exact graph coloring" (PDF), Journal of Graph Algorithms and Applications, 7 (2): 131–140, arXiv:cs.DS/0011009, CiteSeerX 10.1.1.342.4049, doi:10.7155/jgaa.00064.
Bisdorff & Marichal (2008); Euler (2005); Füredi (1987). Bisdorff, Raymond; Marichal, Jean-Luc (2008), "Counting non-isomorphic maximal independent sets of the n-cycle graph", Journal of Integer Sequences, 11: 08.5.7, arXiv:math.CO/0701647. Euler, R. (2005), "The Fibonacci number of a grid graph and a new class of integer sequences", Journal of Integer Sequences, 8 (2): 05.2.6, Bibcode:2005JIntS...8...26E. Füredi, Z. (1987), "The number of maximal independent sets in connected graphs", Journal of Graph Theory, 11 (4): 463–470, doi:10.1002/jgt.3190110403.
Blelloch, Guy; Fineman, Jeremy; Shun, Julian (2012). "Greedy Sequential Maximal Independent Set and Matching are Parallel on Average". arXiv:1202.3205 [cs.DS].
Eppstein (2003); Byskov (2003). Eppstein, D. (2003), "Small maximal independent sets and faster exact graph coloring" (PDF), Journal of Graph Algorithms and Applications, 7 (2): 131–140, arXiv:cs.DS/0011009, CiteSeerX 10.1.1.342.4049, doi:10.7155/jgaa.00064. Byskov, J. M. (2003), "Algorithms for k-colouring and finding maximal independent sets", Proceedings of the Fourteenth Annual ACM-SIAM Symposium on Discrete Algorithms, Soda '03, pp. 456–457, ISBN 9780898715385.
Eppstein (2003). For a matching bound for the widely used Bron–Kerbosch algorithm, see Tomita, Tanaka & Takahashi (2006). Eppstein, D. (2003), "Small maximal independent sets and faster exact graph coloring" (PDF), Journal of Graph Algorithms and Applications, 7 (2): 131–140, arXiv:cs.DS/0011009, CiteSeerX 10.1.1.342.4049, doi:10.7155/jgaa.00064. Tomita, E.; Tanaka, A.; Takahashi, H. (2006), "The worst-case time complexity for generating all maximal cliques and computational experiments", Theoretical Computer Science, 363 (1): 28–42, doi:10.1016/j.tcs.2006.06.015.
Bomze et al. (1999); Eppstein (2005); Jennings & Motycková (1992); Johnson, Yannakakis & Papadimitriou (1988); Lawler, Lenstra & Rinnooy Kan (1980); Liang, Dhall & Lakshmivarahan (1991); Makino & Uno (2004); Mishra & Pitt (1997); Stix (2004); Tsukiyama et al. (1977); Yu & Chen (1993). Bomze, I. M.; Budinich, M.; Pardalos, P. M.; Pelillo, M. (1999), "The maximum clique problem", Handbook of Combinatorial Optimization, vol. 4, Kluwer Academic Publishers, pp. 1–74, CiteSeerX 10.1.1.48.4074. Eppstein, D. (2005), "All maximal independent sets and dynamic dominance for sparse graphs", Proc. Sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms, vol. 5, pp. 451–459, arXiv:cs.DS/0407036, doi:10.1145/1597036.1597042, S2CID 2769046. Jennings, E.; Motycková, L. (1992), "A distributed algorithm for finding all maximal cliques in a network graph", Proc. First Latin American Symposium on Theoretical Informatics, Lecture Notes in Computer Science, vol. 583, Springer-Verlag, pp. 281–293 Johnson, D. S.; Yannakakis, M.; Papadimitriou, C. H. (1988), "On generating all maximal independent sets", Information Processing Letters, 27 (3): 119–123, doi:10.1016/0020-0190(88)90065-8. Lawler, E. L.; Lenstra, J. K.; Rinnooy Kan, A. H. G. (1980), "Generating all maximal independent sets: NP-hardness and polynomial time algorithms" (PDF), SIAM Journal on Computing, 9 (3): 558–565, doi:10.1137/0209042, S2CID 29527771. Liang, Y. D.; Dhall, S. K.; Lakshmivarahan, S. (1991), "On the problem of finding all maximum weight independent sets in interval and circular arc graphs", Proceeding of the 1991 Symposium on Applied Computing, pp. 465–470, doi:10.1109/SOAC.1991.143921, ISBN 0-8186-2136-2, S2CID 122685841 Makino, K.; Uno, T. (2004), "New algorithms for enumerating all maximal cliques", Proc. Ninth Scandinavian Workshop on Algorithm Theory, Lecture Notes in Computer Science, vol. 3111, Springer-Verlag, pp. 260–272, CiteSeerX 10.1.1.138.705, doi:10.1007/978-3-540-27810-8_23, ISBN 978-3-540-22339-9. ISBN 9783540223399, 9783540278108. Mishra, N.; Pitt, L. (1997), "Generating all maximal independent sets of bounded-degree hypergraphs", Proc. Tenth Conf. Computational Learning Theory, pp. 211–217, doi:10.1145/267460.267500, ISBN 978-0-89791-891-6, S2CID 5254186. Stix, V. (2004), "Finding all maximal cliques in dynamic graphs", Computational Optimization and Applications, 27 (2): 173–186, CiteSeerX 10.1.1.497.6424, doi:10.1023/B:COAP.0000008651.28952.b6, S2CID 17824282 Tsukiyama, S.; Ide, M.; Ariyoshi, H.; Shirakawa, I. (1977), "A new algorithm for generating all the maximal independent sets", SIAM Journal on Computing, 6 (3): 505–517, doi:10.1137/0206036. Yu, C.-W.; Chen, G.-H. (1993), "Generate all maximal independent sets in permutation graphs", Internat. J. Comput. Math., 47 (1–2): 1–8, doi:10.1080/00207169308804157.
Makino & Uno (2004); Eppstein (2005). Makino, K.; Uno, T. (2004), "New algorithms for enumerating all maximal cliques", Proc. Ninth Scandinavian Workshop on Algorithm Theory, Lecture Notes in Computer Science, vol. 3111, Springer-Verlag, pp. 260–272, CiteSeerX 10.1.1.138.705, doi:10.1007/978-3-540-27810-8_23, ISBN 978-3-540-22339-9. ISBN 9783540223399, 9783540278108. Eppstein, D. (2005), "All maximal independent sets and dynamic dominance for sparse graphs", Proc. Sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms, vol. 5, pp. 451–459, arXiv:cs.DS/0407036, doi:10.1145/1597036.1597042, S2CID 2769046.

brown.edu

cs.brown.edu

Byskov (2003). For related earlier results see Croitoru (1979) and Eppstein (2003). Byskov, J. M. (2003), "Algorithms for k-colouring and finding maximal independent sets", Proceedings of the Fourteenth Annual ACM-SIAM Symposium on Discrete Algorithms, Soda '03, pp. 456–457, ISBN 9780898715385. Croitoru, C. (1979), "On stables in graphs", Proc. Third Coll. Operations Research, Babeş-Bolyai University, Cluj-Napoca, Romania, pp. 55–60. Eppstein, D. (2003), "Small maximal independent sets and faster exact graph coloring" (PDF), Journal of Graph Algorithms and Applications, 7 (2): 131–140, arXiv:cs.DS/0011009, CiteSeerX 10.1.1.342.4049, doi:10.7155/jgaa.00064.
Eppstein (2003); Byskov (2003). Eppstein, D. (2003), "Small maximal independent sets and faster exact graph coloring" (PDF), Journal of Graph Algorithms and Applications, 7 (2): 131–140, arXiv:cs.DS/0011009, CiteSeerX 10.1.1.342.4049, doi:10.7155/jgaa.00064. Byskov, J. M. (2003), "Algorithms for k-colouring and finding maximal independent sets", Proceedings of the Fourteenth Annual ACM-SIAM Symposium on Discrete Algorithms, Soda '03, pp. 456–457, ISBN 9780898715385.
Eppstein (2003). For a matching bound for the widely used Bron–Kerbosch algorithm, see Tomita, Tanaka & Takahashi (2006). Eppstein, D. (2003), "Small maximal independent sets and faster exact graph coloring" (PDF), Journal of Graph Algorithms and Applications, 7 (2): 131–140, arXiv:cs.DS/0011009, CiteSeerX 10.1.1.342.4049, doi:10.7155/jgaa.00064. Tomita, E.; Tanaka, A.; Takahashi, H. (2006), "The worst-case time complexity for generating all maximal cliques and computational experiments", Theoretical Computer Science, 363 (1): 28–42, doi:10.1016/j.tcs.2006.06.015.

cglab.ca

Barba, Luis (October 2012). "LITERATURE REVIEW: Parallel algorithms for the maximal independent set problem in graphs" (PDF).

doi.org

Erdős (1966) shows that the number of different sizes of MISs in an $n$ -vertex graph may be as large as $n - log n - O (log log n)$ and is never larger than $n - log n$ . Erdős, P. (1966), "On cliques in graphs", Israel Journal of Mathematics, 4 (4): 233–234, doi:10.1007/BF02771637, MR 0205874, S2CID 121993028.
Weigt & Hartmann (2001). Weigt, Martin; Hartmann, Alexander K. (2001), "Minimal vertex covers on finite-connectivity random graphs: A hard-sphere lattice-gas picture", Phys. Rev. E, 63 (5): 056127, arXiv:cond-mat/0011446, Bibcode:2001PhRvE..63e6127W, doi:10.1103/PhysRevE.63.056127, PMID 11414981, S2CID 16773685.
Byskov (2003). For related earlier results see Croitoru (1979) and Eppstein (2003). Byskov, J. M. (2003), "Algorithms for k-colouring and finding maximal independent sets", Proceedings of the Fourteenth Annual ACM-SIAM Symposium on Discrete Algorithms, Soda '03, pp. 456–457, ISBN 9780898715385. Croitoru, C. (1979), "On stables in graphs", Proc. Third Coll. Operations Research, Babeş-Bolyai University, Cluj-Napoca, Romania, pp. 55–60. Eppstein, D. (2003), "Small maximal independent sets and faster exact graph coloring" (PDF), Journal of Graph Algorithms and Applications, 7 (2): 131–140, arXiv:cs.DS/0011009, CiteSeerX 10.1.1.342.4049, doi:10.7155/jgaa.00064.
Chiba & Nishizeki (1985). Chiba and Nishizeki express the condition of having O(n) edges equivalently, in terms of the arboricity of the graphs in the family being constant. Chiba, N.; Nishizeki, T. (1985), "Arboricity and subgraph listing algorithms", SIAM Journal on Computing, 14 (1): 210–223, doi:10.1137/0214017, S2CID 207051803.
Bisdorff & Marichal (2008); Euler (2005); Füredi (1987). Bisdorff, Raymond; Marichal, Jean-Luc (2008), "Counting non-isomorphic maximal independent sets of the n-cycle graph", Journal of Integer Sequences, 11: 08.5.7, arXiv:math.CO/0701647. Euler, R. (2005), "The Fibonacci number of a grid graph and a new class of integer sequences", Journal of Integer Sequences, 8 (2): 05.2.6, Bibcode:2005JIntS...8...26E. Füredi, Z. (1987), "The number of maximal independent sets in connected graphs", Journal of Graph Theory, 11 (4): 463–470, doi:10.1002/jgt.3190110403.
Luby, M. (1986). "A Simple Parallel Algorithm for the Maximal Independent Set Problem". SIAM Journal on Computing. 15 (4): 1036–1053. CiteSeerX 10.1.1.225.5475. doi:10.1137/0215074.
Métivier, Y.; Robson, J. M.; Saheb-Djahromi, N.; Zemmari, A. (2010). "An optimal bit complexity randomized distributed MIS algorithm". Distributed Computing. 23 (5–6): 331. doi:10.1007/s00446-010-0121-5. S2CID 36720853.
Eppstein (2003); Byskov (2003). Eppstein, D. (2003), "Small maximal independent sets and faster exact graph coloring" (PDF), Journal of Graph Algorithms and Applications, 7 (2): 131–140, arXiv:cs.DS/0011009, CiteSeerX 10.1.1.342.4049, doi:10.7155/jgaa.00064. Byskov, J. M. (2003), "Algorithms for k-colouring and finding maximal independent sets", Proceedings of the Fourteenth Annual ACM-SIAM Symposium on Discrete Algorithms, Soda '03, pp. 456–457, ISBN 9780898715385.
Eppstein (2003). For a matching bound for the widely used Bron–Kerbosch algorithm, see Tomita, Tanaka & Takahashi (2006). Eppstein, D. (2003), "Small maximal independent sets and faster exact graph coloring" (PDF), Journal of Graph Algorithms and Applications, 7 (2): 131–140, arXiv:cs.DS/0011009, CiteSeerX 10.1.1.342.4049, doi:10.7155/jgaa.00064. Tomita, E.; Tanaka, A.; Takahashi, H. (2006), "The worst-case time complexity for generating all maximal cliques and computational experiments", Theoretical Computer Science, 363 (1): 28–42, doi:10.1016/j.tcs.2006.06.015.
Bomze et al. (1999); Eppstein (2005); Jennings & Motycková (1992); Johnson, Yannakakis & Papadimitriou (1988); Lawler, Lenstra & Rinnooy Kan (1980); Liang, Dhall & Lakshmivarahan (1991); Makino & Uno (2004); Mishra & Pitt (1997); Stix (2004); Tsukiyama et al. (1977); Yu & Chen (1993). Bomze, I. M.; Budinich, M.; Pardalos, P. M.; Pelillo, M. (1999), "The maximum clique problem", Handbook of Combinatorial Optimization, vol. 4, Kluwer Academic Publishers, pp. 1–74, CiteSeerX 10.1.1.48.4074. Eppstein, D. (2005), "All maximal independent sets and dynamic dominance for sparse graphs", Proc. Sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms, vol. 5, pp. 451–459, arXiv:cs.DS/0407036, doi:10.1145/1597036.1597042, S2CID 2769046. Jennings, E.; Motycková, L. (1992), "A distributed algorithm for finding all maximal cliques in a network graph", Proc. First Latin American Symposium on Theoretical Informatics, Lecture Notes in Computer Science, vol. 583, Springer-Verlag, pp. 281–293 Johnson, D. S.; Yannakakis, M.; Papadimitriou, C. H. (1988), "On generating all maximal independent sets", Information Processing Letters, 27 (3): 119–123, doi:10.1016/0020-0190(88)90065-8. Lawler, E. L.; Lenstra, J. K.; Rinnooy Kan, A. H. G. (1980), "Generating all maximal independent sets: NP-hardness and polynomial time algorithms" (PDF), SIAM Journal on Computing, 9 (3): 558–565, doi:10.1137/0209042, S2CID 29527771. Liang, Y. D.; Dhall, S. K.; Lakshmivarahan, S. (1991), "On the problem of finding all maximum weight independent sets in interval and circular arc graphs", Proceeding of the 1991 Symposium on Applied Computing, pp. 465–470, doi:10.1109/SOAC.1991.143921, ISBN 0-8186-2136-2, S2CID 122685841 Makino, K.; Uno, T. (2004), "New algorithms for enumerating all maximal cliques", Proc. Ninth Scandinavian Workshop on Algorithm Theory, Lecture Notes in Computer Science, vol. 3111, Springer-Verlag, pp. 260–272, CiteSeerX 10.1.1.138.705, doi:10.1007/978-3-540-27810-8_23, ISBN 978-3-540-22339-9. ISBN 9783540223399, 9783540278108. Mishra, N.; Pitt, L. (1997), "Generating all maximal independent sets of bounded-degree hypergraphs", Proc. Tenth Conf. Computational Learning Theory, pp. 211–217, doi:10.1145/267460.267500, ISBN 978-0-89791-891-6, S2CID 5254186. Stix, V. (2004), "Finding all maximal cliques in dynamic graphs", Computational Optimization and Applications, 27 (2): 173–186, CiteSeerX 10.1.1.497.6424, doi:10.1023/B:COAP.0000008651.28952.b6, S2CID 17824282 Tsukiyama, S.; Ide, M.; Ariyoshi, H.; Shirakawa, I. (1977), "A new algorithm for generating all the maximal independent sets", SIAM Journal on Computing, 6 (3): 505–517, doi:10.1137/0206036. Yu, C.-W.; Chen, G.-H. (1993), "Generate all maximal independent sets in permutation graphs", Internat. J. Comput. Math., 47 (1–2): 1–8, doi:10.1080/00207169308804157.
Makino & Uno (2004); Eppstein (2005). Makino, K.; Uno, T. (2004), "New algorithms for enumerating all maximal cliques", Proc. Ninth Scandinavian Workshop on Algorithm Theory, Lecture Notes in Computer Science, vol. 3111, Springer-Verlag, pp. 260–272, CiteSeerX 10.1.1.138.705, doi:10.1007/978-3-540-27810-8_23, ISBN 978-3-540-22339-9. ISBN 9783540223399, 9783540278108. Eppstein, D. (2005), "All maximal independent sets and dynamic dominance for sparse graphs", Proc. Sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms, vol. 5, pp. 451–459, arXiv:cs.DS/0407036, doi:10.1145/1597036.1597042, S2CID 2769046.
Provan, J. Scott; Ball, Michael O. (November 1983). "The Complexity of Counting Cuts and of Computing the Probability that a Graph is Connected". SIAM Journal on Computing. 12 (4): 777–788. doi:10.1137/0212053. ISSN 0097-5397.
Corneil, D. G.; Lerchs, H.; Burlingham, L. Stewart (1981-07-01). "Complement reducible graphs". Discrete Applied Mathematics. 3 (3): 163–174. doi:10.1016/0166-218X(81)90013-5. ISSN 0166-218X.
Cook, Stephen (June 1983). "An overview of computational complexity". Commun. ACM. 26 (6): 400–408. doi:10.1145/358141.358144. S2CID 14323396.
Alon, Noga; Laszlo, Babai; Alon, Itai (1986). "A fast and simple randomized parallel algorithm for the maximal independent set problem". Journal of Algorithms. 7 (4): 567–583. doi:10.1016/0196-6774(86)90019-2.
Peleg, David (2000). Distributed Computing: A Locality-Sensitive Approach. doi:10.1137/1.9780898719772. ISBN 978-0-89871-464-7.

ethz.ch

dcg.ethz.ch

"Principles of Distributed Computing (lecture 7)" (PDF). ETH Zurich. Archived from the original (PDF) on 21 February 2015. Retrieved 21 February 2015.
Wattenhofer, R. "Chapter 4: Maximal Independent Set" (PDF).

gatech.edu

cc.gatech.edu

Luby’s Algorithm, in: Lecture Notes for Randomized Algorithms, Last Updated by Eric Vigoda on February 2, 2006

harvard.edu

ui.adsabs.harvard.edu

Weigt & Hartmann (2001). Weigt, Martin; Hartmann, Alexander K. (2001), "Minimal vertex covers on finite-connectivity random graphs: A hard-sphere lattice-gas picture", Phys. Rev. E, 63 (5): 056127, arXiv:cond-mat/0011446, Bibcode:2001PhRvE..63e6127W, doi:10.1103/PhysRevE.63.056127, PMID 11414981, S2CID 16773685.
Bisdorff & Marichal (2008); Euler (2005); Füredi (1987). Bisdorff, Raymond; Marichal, Jean-Luc (2008), "Counting non-isomorphic maximal independent sets of the n-cycle graph", Journal of Integer Sequences, 11: 08.5.7, arXiv:math.CO/0701647. Euler, R. (2005), "The Fibonacci number of a grid graph and a new class of integer sequences", Journal of Integer Sequences, 8 (2): 05.2.6, Bibcode:2005JIntS...8...26E. Füredi, Z. (1987), "The number of maximal independent sets in connected graphs", Journal of Graph Theory, 11 (4): 463–470, doi:10.1002/jgt.3190110403.

nih.gov

pubmed.ncbi.nlm.nih.gov

Weigt & Hartmann (2001). Weigt, Martin; Hartmann, Alexander K. (2001), "Minimal vertex covers on finite-connectivity random graphs: A hard-sphere lattice-gas picture", Phys. Rev. E, 63 (5): 056127, arXiv:cond-mat/0011446, Bibcode:2001PhRvE..63e6127W, doi:10.1103/PhysRevE.63.056127, PMID 11414981, S2CID 16773685.

psu.edu

citeseerx.ist.psu.edu

Byskov (2003). For related earlier results see Croitoru (1979) and Eppstein (2003). Byskov, J. M. (2003), "Algorithms for k-colouring and finding maximal independent sets", Proceedings of the Fourteenth Annual ACM-SIAM Symposium on Discrete Algorithms, Soda '03, pp. 456–457, ISBN 9780898715385. Croitoru, C. (1979), "On stables in graphs", Proc. Third Coll. Operations Research, Babeş-Bolyai University, Cluj-Napoca, Romania, pp. 55–60. Eppstein, D. (2003), "Small maximal independent sets and faster exact graph coloring" (PDF), Journal of Graph Algorithms and Applications, 7 (2): 131–140, arXiv:cs.DS/0011009, CiteSeerX 10.1.1.342.4049, doi:10.7155/jgaa.00064.
Luby, M. (1986). "A Simple Parallel Algorithm for the Maximal Independent Set Problem". SIAM Journal on Computing. 15 (4): 1036–1053. CiteSeerX 10.1.1.225.5475. doi:10.1137/0215074.
Eppstein (2003); Byskov (2003). Eppstein, D. (2003), "Small maximal independent sets and faster exact graph coloring" (PDF), Journal of Graph Algorithms and Applications, 7 (2): 131–140, arXiv:cs.DS/0011009, CiteSeerX 10.1.1.342.4049, doi:10.7155/jgaa.00064. Byskov, J. M. (2003), "Algorithms for k-colouring and finding maximal independent sets", Proceedings of the Fourteenth Annual ACM-SIAM Symposium on Discrete Algorithms, Soda '03, pp. 456–457, ISBN 9780898715385.
Eppstein (2003). For a matching bound for the widely used Bron–Kerbosch algorithm, see Tomita, Tanaka & Takahashi (2006). Eppstein, D. (2003), "Small maximal independent sets and faster exact graph coloring" (PDF), Journal of Graph Algorithms and Applications, 7 (2): 131–140, arXiv:cs.DS/0011009, CiteSeerX 10.1.1.342.4049, doi:10.7155/jgaa.00064. Tomita, E.; Tanaka, A.; Takahashi, H. (2006), "The worst-case time complexity for generating all maximal cliques and computational experiments", Theoretical Computer Science, 363 (1): 28–42, doi:10.1016/j.tcs.2006.06.015.
Bomze et al. (1999); Eppstein (2005); Jennings & Motycková (1992); Johnson, Yannakakis & Papadimitriou (1988); Lawler, Lenstra & Rinnooy Kan (1980); Liang, Dhall & Lakshmivarahan (1991); Makino & Uno (2004); Mishra & Pitt (1997); Stix (2004); Tsukiyama et al. (1977); Yu & Chen (1993). Bomze, I. M.; Budinich, M.; Pardalos, P. M.; Pelillo, M. (1999), "The maximum clique problem", Handbook of Combinatorial Optimization, vol. 4, Kluwer Academic Publishers, pp. 1–74, CiteSeerX 10.1.1.48.4074. Eppstein, D. (2005), "All maximal independent sets and dynamic dominance for sparse graphs", Proc. Sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms, vol. 5, pp. 451–459, arXiv:cs.DS/0407036, doi:10.1145/1597036.1597042, S2CID 2769046. Jennings, E.; Motycková, L. (1992), "A distributed algorithm for finding all maximal cliques in a network graph", Proc. First Latin American Symposium on Theoretical Informatics, Lecture Notes in Computer Science, vol. 583, Springer-Verlag, pp. 281–293 Johnson, D. S.; Yannakakis, M.; Papadimitriou, C. H. (1988), "On generating all maximal independent sets", Information Processing Letters, 27 (3): 119–123, doi:10.1016/0020-0190(88)90065-8. Lawler, E. L.; Lenstra, J. K.; Rinnooy Kan, A. H. G. (1980), "Generating all maximal independent sets: NP-hardness and polynomial time algorithms" (PDF), SIAM Journal on Computing, 9 (3): 558–565, doi:10.1137/0209042, S2CID 29527771. Liang, Y. D.; Dhall, S. K.; Lakshmivarahan, S. (1991), "On the problem of finding all maximum weight independent sets in interval and circular arc graphs", Proceeding of the 1991 Symposium on Applied Computing, pp. 465–470, doi:10.1109/SOAC.1991.143921, ISBN 0-8186-2136-2, S2CID 122685841 Makino, K.; Uno, T. (2004), "New algorithms for enumerating all maximal cliques", Proc. Ninth Scandinavian Workshop on Algorithm Theory, Lecture Notes in Computer Science, vol. 3111, Springer-Verlag, pp. 260–272, CiteSeerX 10.1.1.138.705, doi:10.1007/978-3-540-27810-8_23, ISBN 978-3-540-22339-9. ISBN 9783540223399, 9783540278108. Mishra, N.; Pitt, L. (1997), "Generating all maximal independent sets of bounded-degree hypergraphs", Proc. Tenth Conf. Computational Learning Theory, pp. 211–217, doi:10.1145/267460.267500, ISBN 978-0-89791-891-6, S2CID 5254186. Stix, V. (2004), "Finding all maximal cliques in dynamic graphs", Computational Optimization and Applications, 27 (2): 173–186, CiteSeerX 10.1.1.497.6424, doi:10.1023/B:COAP.0000008651.28952.b6, S2CID 17824282 Tsukiyama, S.; Ide, M.; Ariyoshi, H.; Shirakawa, I. (1977), "A new algorithm for generating all the maximal independent sets", SIAM Journal on Computing, 6 (3): 505–517, doi:10.1137/0206036. Yu, C.-W.; Chen, G.-H. (1993), "Generate all maximal independent sets in permutation graphs", Internat. J. Comput. Math., 47 (1–2): 1–8, doi:10.1080/00207169308804157.
Makino & Uno (2004); Eppstein (2005). Makino, K.; Uno, T. (2004), "New algorithms for enumerating all maximal cliques", Proc. Ninth Scandinavian Workshop on Algorithm Theory, Lecture Notes in Computer Science, vol. 3111, Springer-Verlag, pp. 260–272, CiteSeerX 10.1.1.138.705, doi:10.1007/978-3-540-27810-8_23, ISBN 978-3-540-22339-9. ISBN 9783540223399, 9783540278108. Eppstein, D. (2005), "All maximal independent sets and dynamic dominance for sparse graphs", Proc. Sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms, vol. 5, pp. 451–459, arXiv:cs.DS/0407036, doi:10.1145/1597036.1597042, S2CID 2769046.

sciencedirect.com

Corneil, D. G.; Lerchs, H.; Burlingham, L. Stewart (1981-07-01). "Complement reducible graphs". Discrete Applied Mathematics. 3 (3): 163–174. doi:10.1016/0166-218X(81)90013-5. ISSN 0166-218X.

semanticscholar.org

api.semanticscholar.org

Erdős (1966) shows that the number of different sizes of MISs in an $n$ -vertex graph may be as large as $n - log n - O (log log n)$ and is never larger than $n - log n$ . Erdős, P. (1966), "On cliques in graphs", Israel Journal of Mathematics, 4 (4): 233–234, doi:10.1007/BF02771637, MR 0205874, S2CID 121993028.
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Chiba & Nishizeki (1985). Chiba and Nishizeki express the condition of having O(n) edges equivalently, in terms of the arboricity of the graphs in the family being constant. Chiba, N.; Nishizeki, T. (1985), "Arboricity and subgraph listing algorithms", SIAM Journal on Computing, 14 (1): 210–223, doi:10.1137/0214017, S2CID 207051803.
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Bomze et al. (1999); Eppstein (2005); Jennings & Motycková (1992); Johnson, Yannakakis & Papadimitriou (1988); Lawler, Lenstra & Rinnooy Kan (1980); Liang, Dhall & Lakshmivarahan (1991); Makino & Uno (2004); Mishra & Pitt (1997); Stix (2004); Tsukiyama et al. (1977); Yu & Chen (1993). Bomze, I. M.; Budinich, M.; Pardalos, P. M.; Pelillo, M. (1999), "The maximum clique problem", Handbook of Combinatorial Optimization, vol. 4, Kluwer Academic Publishers, pp. 1–74, CiteSeerX 10.1.1.48.4074. Eppstein, D. (2005), "All maximal independent sets and dynamic dominance for sparse graphs", Proc. Sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms, vol. 5, pp. 451–459, arXiv:cs.DS/0407036, doi:10.1145/1597036.1597042, S2CID 2769046. Jennings, E.; Motycková, L. (1992), "A distributed algorithm for finding all maximal cliques in a network graph", Proc. First Latin American Symposium on Theoretical Informatics, Lecture Notes in Computer Science, vol. 583, Springer-Verlag, pp. 281–293 Johnson, D. S.; Yannakakis, M.; Papadimitriou, C. H. (1988), "On generating all maximal independent sets", Information Processing Letters, 27 (3): 119–123, doi:10.1016/0020-0190(88)90065-8. Lawler, E. L.; Lenstra, J. K.; Rinnooy Kan, A. H. G. (1980), "Generating all maximal independent sets: NP-hardness and polynomial time algorithms" (PDF), SIAM Journal on Computing, 9 (3): 558–565, doi:10.1137/0209042, S2CID 29527771. Liang, Y. D.; Dhall, S. K.; Lakshmivarahan, S. (1991), "On the problem of finding all maximum weight independent sets in interval and circular arc graphs", Proceeding of the 1991 Symposium on Applied Computing, pp. 465–470, doi:10.1109/SOAC.1991.143921, ISBN 0-8186-2136-2, S2CID 122685841 Makino, K.; Uno, T. (2004), "New algorithms for enumerating all maximal cliques", Proc. Ninth Scandinavian Workshop on Algorithm Theory, Lecture Notes in Computer Science, vol. 3111, Springer-Verlag, pp. 260–272, CiteSeerX 10.1.1.138.705, doi:10.1007/978-3-540-27810-8_23, ISBN 978-3-540-22339-9. ISBN 9783540223399, 9783540278108. Mishra, N.; Pitt, L. (1997), "Generating all maximal independent sets of bounded-degree hypergraphs", Proc. Tenth Conf. Computational Learning Theory, pp. 211–217, doi:10.1145/267460.267500, ISBN 978-0-89791-891-6, S2CID 5254186. Stix, V. (2004), "Finding all maximal cliques in dynamic graphs", Computational Optimization and Applications, 27 (2): 173–186, CiteSeerX 10.1.1.497.6424, doi:10.1023/B:COAP.0000008651.28952.b6, S2CID 17824282 Tsukiyama, S.; Ide, M.; Ariyoshi, H.; Shirakawa, I. (1977), "A new algorithm for generating all the maximal independent sets", SIAM Journal on Computing, 6 (3): 505–517, doi:10.1137/0206036. Yu, C.-W.; Chen, G.-H. (1993), "Generate all maximal independent sets in permutation graphs", Internat. J. Comput. Math., 47 (1–2): 1–8, doi:10.1080/00207169308804157.
Makino & Uno (2004); Eppstein (2005). Makino, K.; Uno, T. (2004), "New algorithms for enumerating all maximal cliques", Proc. Ninth Scandinavian Workshop on Algorithm Theory, Lecture Notes in Computer Science, vol. 3111, Springer-Verlag, pp. 260–272, CiteSeerX 10.1.1.138.705, doi:10.1007/978-3-540-27810-8_23, ISBN 978-3-540-22339-9. ISBN 9783540223399, 9783540278108. Eppstein, D. (2005), "All maximal independent sets and dynamic dominance for sparse graphs", Proc. Sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms, vol. 5, pp. 451–459, arXiv:cs.DS/0407036, doi:10.1145/1597036.1597042, S2CID 2769046.
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siam.org

epubs.siam.org

Provan, J. Scott; Ball, Michael O. (November 1983). "The Complexity of Counting Cuts and of Computing the Probability that a Graph is Connected". SIAM Journal on Computing. 12 (4): 777–788. doi:10.1137/0212053. ISSN 0097-5397.

tue.nl

pure.tue.nl

Bomze et al. (1999); Eppstein (2005); Jennings & Motycková (1992); Johnson, Yannakakis & Papadimitriou (1988); Lawler, Lenstra & Rinnooy Kan (1980); Liang, Dhall & Lakshmivarahan (1991); Makino & Uno (2004); Mishra & Pitt (1997); Stix (2004); Tsukiyama et al. (1977); Yu & Chen (1993). Bomze, I. M.; Budinich, M.; Pardalos, P. M.; Pelillo, M. (1999), "The maximum clique problem", Handbook of Combinatorial Optimization, vol. 4, Kluwer Academic Publishers, pp. 1–74, CiteSeerX 10.1.1.48.4074. Eppstein, D. (2005), "All maximal independent sets and dynamic dominance for sparse graphs", Proc. Sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms, vol. 5, pp. 451–459, arXiv:cs.DS/0407036, doi:10.1145/1597036.1597042, S2CID 2769046. Jennings, E.; Motycková, L. (1992), "A distributed algorithm for finding all maximal cliques in a network graph", Proc. First Latin American Symposium on Theoretical Informatics, Lecture Notes in Computer Science, vol. 583, Springer-Verlag, pp. 281–293 Johnson, D. S.; Yannakakis, M.; Papadimitriou, C. H. (1988), "On generating all maximal independent sets", Information Processing Letters, 27 (3): 119–123, doi:10.1016/0020-0190(88)90065-8. Lawler, E. L.; Lenstra, J. K.; Rinnooy Kan, A. H. G. (1980), "Generating all maximal independent sets: NP-hardness and polynomial time algorithms" (PDF), SIAM Journal on Computing, 9 (3): 558–565, doi:10.1137/0209042, S2CID 29527771. Liang, Y. D.; Dhall, S. K.; Lakshmivarahan, S. (1991), "On the problem of finding all maximum weight independent sets in interval and circular arc graphs", Proceeding of the 1991 Symposium on Applied Computing, pp. 465–470, doi:10.1109/SOAC.1991.143921, ISBN 0-8186-2136-2, S2CID 122685841 Makino, K.; Uno, T. (2004), "New algorithms for enumerating all maximal cliques", Proc. Ninth Scandinavian Workshop on Algorithm Theory, Lecture Notes in Computer Science, vol. 3111, Springer-Verlag, pp. 260–272, CiteSeerX 10.1.1.138.705, doi:10.1007/978-3-540-27810-8_23, ISBN 978-3-540-22339-9. ISBN 9783540223399, 9783540278108. Mishra, N.; Pitt, L. (1997), "Generating all maximal independent sets of bounded-degree hypergraphs", Proc. Tenth Conf. Computational Learning Theory, pp. 211–217, doi:10.1145/267460.267500, ISBN 978-0-89791-891-6, S2CID 5254186. Stix, V. (2004), "Finding all maximal cliques in dynamic graphs", Computational Optimization and Applications, 27 (2): 173–186, CiteSeerX 10.1.1.497.6424, doi:10.1023/B:COAP.0000008651.28952.b6, S2CID 17824282 Tsukiyama, S.; Ide, M.; Ariyoshi, H.; Shirakawa, I. (1977), "A new algorithm for generating all the maximal independent sets", SIAM Journal on Computing, 6 (3): 505–517, doi:10.1137/0206036. Yu, C.-W.; Chen, G.-H. (1993), "Generate all maximal independent sets in permutation graphs", Internat. J. Comput. Math., 47 (1–2): 1–8, doi:10.1080/00207169308804157.

uni-rostock.de

wwwteo.informatik.uni-rostock.de

Information System on Graph Class Inclusions: maximal clique irreducible graphs Archived 2007-07-09 at the Wayback Machine and hereditary maximal clique irreducible graphs Archived 2007-07-08 at the Wayback Machine.

uwaterloo.ca

cs.uwaterloo.ca

Bisdorff & Marichal (2008); Euler (2005); Füredi (1987). Bisdorff, Raymond; Marichal, Jean-Luc (2008), "Counting non-isomorphic maximal independent sets of the n-cycle graph", Journal of Integer Sequences, 11: 08.5.7, arXiv:math.CO/0701647. Euler, R. (2005), "The Fibonacci number of a grid graph and a new class of integer sequences", Journal of Integer Sequences, 8 (2): 05.2.6, Bibcode:2005JIntS...8...26E. Füredi, Z. (1987), "The number of maximal independent sets in connected graphs", Journal of Graph Theory, 11 (4): 463–470, doi:10.1002/jgt.3190110403.

web.archive.org

Information System on Graph Class Inclusions: maximal clique irreducible graphs Archived 2007-07-09 at the Wayback Machine and hereditary maximal clique irreducible graphs Archived 2007-07-08 at the Wayback Machine.
"Principles of Distributed Computing (lecture 7)" (PDF). ETH Zurich. Archived from the original (PDF) on 21 February 2015. Retrieved 21 February 2015.

worldcat.org

search.worldcat.org

Provan, J. Scott; Ball, Michael O. (November 1983). "The Complexity of Counting Cuts and of Computing the Probability that a Graph is Connected". SIAM Journal on Computing. 12 (4): 777–788. doi:10.1137/0212053. ISSN 0097-5397.
Corneil, D. G.; Lerchs, H.; Burlingham, L. Stewart (1981-07-01). "Complement reducible graphs". Discrete Applied Mathematics. 3 (3): 163–174. doi:10.1016/0166-218X(81)90013-5. ISSN 0166-218X.