Cycle basis (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Cycle basis" in English language version.

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26doi.org

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13ams.org

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6nih.gov

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4psu.edu

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2books.google.com

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mathscinet.ams.org

Liebchen, Christian; Rizzi, Romeo (2007), "Classes of cycle bases", Discrete Applied Mathematics, 155 (3): 337–355, doi:10.1016/j.dam.2006.06.007, MR 2303157.
Tutte, W. T. (1963), "How to draw a graph", Proceedings of the London Mathematical Society, Third Series, 13: 743–767, doi:10.1112/plms/s3-13.1.743, MR 0158387. See in particular Theorem 2.5.
Cribb, D. W.; Ringeisen, R. D.; Shier, D. R. (1981), "On cycle bases of a graph", Proceedings of the Twelfth Southeastern Conference on Combinatorics, Graph Theory and Computing, Vol. I (Baton Rouge, La., 1981), Congressus Numerantium, vol. 32, pp. 221–229, MR 0681883.
Rizzi, Romeo (2009), "Minimum weakly fundamental cycle bases are hard to find", Algorithmica, 53 (3): 402–424, doi:10.1007/s00453-007-9112-8, MR 2482112, S2CID 12675654.
Hartvigsen, David; Zemel, Eitan (1989), "Is every cycle basis fundamental?", Journal of Graph Theory, 13 (1): 117–137, doi:10.1002/jgt.3190130115, MR 0982873.
Chickering, David M.; Geiger, Dan; Heckerman, David (1995), "On finding a cycle basis with a shortest maximal cycle", Information Processing Letters, 54 (1): 55–58, CiteSeerX 10.1.1.650.8218, doi:10.1016/0020-0190(94)00231-M, MR 1332422.
Berger, Franziska; Gritzmann, Peter; de Vries, Sven (2004), "Minimum cycle bases for network graphs", Algorithmica, 40 (1): 51–62, doi:10.1007/s00453-004-1098-x, MR 2071255, S2CID 9386078.
Kavitha, Telikepalli; Mehlhorn, Kurt; Michail, Dimitrios; Paluch, Katarzyna E. (2008), "An ${\tilde {O}}(m^{2}n)$ algorithm for minimum cycle basis of graphs", Algorithmica, 52 (3): 333–349, doi:10.1007/s00453-007-9064-z, MR 2452919.
Amaldi, Edoardo; Iuliano, Claudio; Rizzi, Romeo (2010), "Efficient deterministic algorithms for finding a minimum cycle basis in undirected graphs", Integer Programming and Combinatorial Optimization: 14th International Conference, IPCO 2010, Lausanne, Switzerland, June 9-11, 2010, Proceedings, Lecture Notes in Computer Science, vol. 6080, Springer, pp. 397–410, Bibcode:2010LNCS.6080..397A, doi:10.1007/978-3-642-13036-6_30, ISBN 978-3-642-13035-9, MR 2661113.
Deo, Narsingh; Prabhu, G. M.; Krishnamoorthy, M. S. (1982), "Algorithms for generating fundamental cycles in a graph", ACM Transactions on Mathematical Software, 8 (1): 26–42, doi:10.1145/355984.355988, MR 0661120, S2CID 2260051.
Galbiati, Giulia; Amaldi, Edoardo (2004), "On the approximability of the minimum fundamental cycle basis problem", Approximation and Online Algorithms: First International Workshop, WAOA 2003, Budapest, Hungary, September 16-18, 2003, Revised Papers, Lecture Notes in Computer Science, vol. 2909, Berlin: Springer, pp. 151–164, doi:10.1007/978-3-540-24592-6_12, ISBN 978-3-540-21079-5, MR 2089904.
Hartvigsen, David; Mardon, Russell (1994), "The all-pairs min cut problem and the minimum cycle basis problem on planar graphs", SIAM Journal on Discrete Mathematics, 7 (3): 403–418, doi:10.1137/S0895480190177042, MR 1285579.
Gotsman, Craig; Kaligosi, Kanela; Mehlhorn, Kurt; Michail, Dimitrios; Pyrga, Evangelia (2007), "Cycle bases of graphs and sampled manifolds", Computer Aided Geometric Design, 24 (8–9): 464–480, CiteSeerX 10.1.1.298.9661, doi:10.1016/j.cagd.2006.07.001, MR 2359763.

arxiv.org

Borradaile, Glencora; Eppstein, David; Nayyeri, Amir; Wulff-Nilsen, Christian (2016), "All-pairs minimum cuts in near-linear time for surface-embedded graphs", Proc. 32nd Int. Symp. Computational Geometry, Leibniz International Proceedings in Informatics (LIPIcs), vol. 51, Schloss Dagstuhl, pp. 22:1–22:16, arXiv:1411.7055, doi:10.4230/LIPIcs.SoCG.2016.22, S2CID 215762172.

books.google.com

Diestel, Reinhard (2012), "1.9 Some linear algebra", Graph Theory, Graduate Texts in Mathematics, vol. 173, Springer, pp. 23–28.
Gross, Jonathan L.; Yellen, Jay (2005), "4.6 Graphs and Vector Spaces", Graph Theory and Its Applications (2nd ed.), CRC Press, pp. 197–207, ISBN 9781584885054.

doi.org

Liebchen, Christian; Rizzi, Romeo (2007), "Classes of cycle bases", Discrete Applied Mathematics, 155 (3): 337–355, doi:10.1016/j.dam.2006.06.007, MR 2303157.
Tutte, W. T. (1963), "How to draw a graph", Proceedings of the London Mathematical Society, Third Series, 13: 743–767, doi:10.1112/plms/s3-13.1.743, MR 0158387. See in particular Theorem 2.5.
Rizzi, Romeo (2009), "Minimum weakly fundamental cycle bases are hard to find", Algorithmica, 53 (3): 402–424, doi:10.1007/s00453-007-9112-8, MR 2482112, S2CID 12675654.
Hartvigsen, David; Zemel, Eitan (1989), "Is every cycle basis fundamental?", Journal of Graph Theory, 13 (1): 117–137, doi:10.1002/jgt.3190130115, MR 0982873.
Mac Lane, S. (1937), "A combinatorial condition for planar graphs" (PDF), Fundamenta Mathematicae, 28: 22–32, doi:10.4064/fm-28-1-22-32.
Veblen, Oswald (1912), "An application of modular equations in analysis situs", Annals of Mathematics, Second Series, 14 (1): 86–94, doi:10.2307/1967604, JSTOR 1967604.
Chickering, David M.; Geiger, Dan; Heckerman, David (1995), "On finding a cycle basis with a shortest maximal cycle", Information Processing Letters, 54 (1): 55–58, CiteSeerX 10.1.1.650.8218, doi:10.1016/0020-0190(94)00231-M, MR 1332422.
Horton, J. D. (1987), "A polynomial-time algorithm to find the shortest cycle basis of a graph", SIAM Journal on Computing, 16 (2): 358–366, doi:10.1137/0216026.
Berger, Franziska; Gritzmann, Peter; de Vries, Sven (2004), "Minimum cycle bases for network graphs", Algorithmica, 40 (1): 51–62, doi:10.1007/s00453-004-1098-x, MR 2071255, S2CID 9386078.
Mehlhorn, Kurt; Michail, Dimitrios (2006), "Implementing minimum cycle basis algorithms", ACM Journal of Experimental Algorithmics, 11: 2.5, CiteSeerX 10.1.1.60.1087, doi:10.1145/1187436.1216582, S2CID 6198296.
Kavitha, Telikepalli; Mehlhorn, Kurt; Michail, Dimitrios; Paluch, Katarzyna E. (2008), "An ${\tilde {O}}(m^{2}n)$ algorithm for minimum cycle basis of graphs", Algorithmica, 52 (3): 333–349, doi:10.1007/s00453-007-9064-z, MR 2452919.
Kavitha, Telikepalli; Liebchen, Christian; Mehlhorn, Kurt; Michail, Dimitrios; Rizzi, Romeo; Ueckerdt, Torsten; Zweig, Katharina A. (2009), "Cycle bases in graphs: Characterization, algorithms, complexity, and applications", Computer Science Review, 3 (4): 199–243, doi:10.1016/j.cosrev.2009.08.001.
Amaldi, Edoardo; Iuliano, Claudio; Rizzi, Romeo (2010), "Efficient deterministic algorithms for finding a minimum cycle basis in undirected graphs", Integer Programming and Combinatorial Optimization: 14th International Conference, IPCO 2010, Lausanne, Switzerland, June 9-11, 2010, Proceedings, Lecture Notes in Computer Science, vol. 6080, Springer, pp. 397–410, Bibcode:2010LNCS.6080..397A, doi:10.1007/978-3-642-13036-6_30, ISBN 978-3-642-13035-9, MR 2661113.
Deo, Narsingh; Prabhu, G. M.; Krishnamoorthy, M. S. (1982), "Algorithms for generating fundamental cycles in a graph", ACM Transactions on Mathematical Software, 8 (1): 26–42, doi:10.1145/355984.355988, MR 0661120, S2CID 2260051.
Galbiati, Giulia; Amaldi, Edoardo (2004), "On the approximability of the minimum fundamental cycle basis problem", Approximation and Online Algorithms: First International Workshop, WAOA 2003, Budapest, Hungary, September 16-18, 2003, Revised Papers, Lecture Notes in Computer Science, vol. 2909, Berlin: Springer, pp. 151–164, doi:10.1007/978-3-540-24592-6_12, ISBN 978-3-540-21079-5, MR 2089904.
Hartvigsen, David; Mardon, Russell (1994), "The all-pairs min cut problem and the minimum cycle basis problem on planar graphs", SIAM Journal on Discrete Mathematics, 7 (3): 403–418, doi:10.1137/S0895480190177042, MR 1285579.
Borradaile, Glencora; Eppstein, David; Nayyeri, Amir; Wulff-Nilsen, Christian (2016), "All-pairs minimum cuts in near-linear time for surface-embedded graphs", Proc. 32nd Int. Symp. Computational Geometry, Leibniz International Proceedings in Informatics (LIPIcs), vol. 51, Schloss Dagstuhl, pp. 22:1–22:16, arXiv:1411.7055, doi:10.4230/LIPIcs.SoCG.2016.22, S2CID 215762172.
Liebchen, Christian (2007), "Periodic Timetable Optimization in Public Transport", Operations Research Proceedings 2006, vol. 2006, pp. 29–36, doi:10.1007/978-3-540-69995-8_5, ISBN 978-3-540-69994-1.
Cassell, A. C.; De Henderson, J. C.; Kaveh, A. (1974), "Cycle bases for the flexibility analysis of structures", International Journal for Numerical Methods in Engineering, 8 (3): 521–528, Bibcode:1974IJNME...8..521C, doi:10.1002/nme.1620080308.
Boulinier, Christian; Petit, Franck; Villain, Vincent (2004), "When graph theory helps self-stabilization", Proceedings of the Twenty-Third Annual ACM Symposium on Principles of Distributed Computing (PODC '04), New York, NY, USA: ACM, pp. 150–159, CiteSeerX 10.1.1.79.2190, doi:10.1145/1011767.1011790, ISBN 978-1581138023, S2CID 14936510.
Aguiar, Derek; Istrail, Sorin (2012), "HapCompass: A Fast Cycle Basis Algorithm for Accurate Haplotype Assembly of Sequence Data", Journal of Computational Biology, 19 (6): 577–590, doi:10.1089/cmb.2012.0084, PMC 3375639, PMID 22697235.
Lemieux, Sébastien; Major, François (2006), "Automated extraction and classification of RNA tertiary structure cyclic motifs", Nucleic Acids Research, 34 (8): 2340–2346, doi:10.1093/nar/gkl120, PMC 1458283, PMID 16679452.
Gotsman, Craig; Kaligosi, Kanela; Mehlhorn, Kurt; Michail, Dimitrios; Pyrga, Evangelia (2007), "Cycle bases of graphs and sampled manifolds", Computer Aided Geometric Design, 24 (8–9): 464–480, CiteSeerX 10.1.1.298.9661, doi:10.1016/j.cagd.2006.07.001, MR 2359763.
May, John W.; Steinbeck, Christoph (2014), "Efficient ring perception for the Chemistry Development Kit", Journal of Cheminformatics, 6 (3): 3, doi:10.1186/1758-2946-6-3, PMC 3922685, PMID 24479757
Downs, G.M.; Gillet, V.J.; Holliday, J.D.; Lynch, M.F. (1989), "A review of ring perception algorithms for chemical graphs", J. Chem. Inf. Comput. Sci., 29 (3): 172–187, doi:10.1021/ci00063a007
Zamora, A. (1979), "An algorithm for finding the smallest set of smallest rings", J. Chem. Inf. Comput. Sci., 16 (1): 40–43, doi:10.1021/ci60005a013

harvard.edu

ui.adsabs.harvard.edu

Amaldi, Edoardo; Iuliano, Claudio; Rizzi, Romeo (2010), "Efficient deterministic algorithms for finding a minimum cycle basis in undirected graphs", Integer Programming and Combinatorial Optimization: 14th International Conference, IPCO 2010, Lausanne, Switzerland, June 9-11, 2010, Proceedings, Lecture Notes in Computer Science, vol. 6080, Springer, pp. 397–410, Bibcode:2010LNCS.6080..397A, doi:10.1007/978-3-642-13036-6_30, ISBN 978-3-642-13035-9, MR 2661113.
Cassell, A. C.; De Henderson, J. C.; Kaveh, A. (1974), "Cycle bases for the flexibility analysis of structures", International Journal for Numerical Methods in Engineering, 8 (3): 521–528, Bibcode:1974IJNME...8..521C, doi:10.1002/nme.1620080308.

icm.edu.pl

matwbn.icm.edu.pl

Mac Lane, S. (1937), "A combinatorial condition for planar graphs" (PDF), Fundamenta Mathematicae, 28: 22–32, doi:10.4064/fm-28-1-22-32.

jstor.org

Veblen, Oswald (1912), "An application of modular equations in analysis situs", Annals of Mathematics, Second Series, 14 (1): 86–94, doi:10.2307/1967604, JSTOR 1967604.

mpg.de

edoc.mpg.de

Mehlhorn, Kurt; Michail, Dimitrios (2006), "Implementing minimum cycle basis algorithms", ACM Journal of Experimental Algorithmics, 11: 2.5, CiteSeerX 10.1.1.60.1087, doi:10.1145/1187436.1216582, S2CID 6198296.
Kavitha, Telikepalli; Liebchen, Christian; Mehlhorn, Kurt; Michail, Dimitrios; Rizzi, Romeo; Ueckerdt, Torsten; Zweig, Katharina A. (2009), "Cycle bases in graphs: Characterization, algorithms, complexity, and applications", Computer Science Review, 3 (4): 199–243, doi:10.1016/j.cosrev.2009.08.001.

nih.gov

ncbi.nlm.nih.gov

Aguiar, Derek; Istrail, Sorin (2012), "HapCompass: A Fast Cycle Basis Algorithm for Accurate Haplotype Assembly of Sequence Data", Journal of Computational Biology, 19 (6): 577–590, doi:10.1089/cmb.2012.0084, PMC 3375639, PMID 22697235.
Lemieux, Sébastien; Major, François (2006), "Automated extraction and classification of RNA tertiary structure cyclic motifs", Nucleic Acids Research, 34 (8): 2340–2346, doi:10.1093/nar/gkl120, PMC 1458283, PMID 16679452.
May, John W.; Steinbeck, Christoph (2014), "Efficient ring perception for the Chemistry Development Kit", Journal of Cheminformatics, 6 (3): 3, doi:10.1186/1758-2946-6-3, PMC 3922685, PMID 24479757

pubmed.ncbi.nlm.nih.gov

Aguiar, Derek; Istrail, Sorin (2012), "HapCompass: A Fast Cycle Basis Algorithm for Accurate Haplotype Assembly of Sequence Data", Journal of Computational Biology, 19 (6): 577–590, doi:10.1089/cmb.2012.0084, PMC 3375639, PMID 22697235.
Lemieux, Sébastien; Major, François (2006), "Automated extraction and classification of RNA tertiary structure cyclic motifs", Nucleic Acids Research, 34 (8): 2340–2346, doi:10.1093/nar/gkl120, PMC 1458283, PMID 16679452.
May, John W.; Steinbeck, Christoph (2014), "Efficient ring perception for the Chemistry Development Kit", Journal of Cheminformatics, 6 (3): 3, doi:10.1186/1758-2946-6-3, PMC 3922685, PMID 24479757

psu.edu

citeseerx.ist.psu.edu

Chickering, David M.; Geiger, Dan; Heckerman, David (1995), "On finding a cycle basis with a shortest maximal cycle", Information Processing Letters, 54 (1): 55–58, CiteSeerX 10.1.1.650.8218, doi:10.1016/0020-0190(94)00231-M, MR 1332422.
Mehlhorn, Kurt; Michail, Dimitrios (2006), "Implementing minimum cycle basis algorithms", ACM Journal of Experimental Algorithmics, 11: 2.5, CiteSeerX 10.1.1.60.1087, doi:10.1145/1187436.1216582, S2CID 6198296.
Boulinier, Christian; Petit, Franck; Villain, Vincent (2004), "When graph theory helps self-stabilization", Proceedings of the Twenty-Third Annual ACM Symposium on Principles of Distributed Computing (PODC '04), New York, NY, USA: ACM, pp. 150–159, CiteSeerX 10.1.1.79.2190, doi:10.1145/1011767.1011790, ISBN 978-1581138023, S2CID 14936510.
Gotsman, Craig; Kaligosi, Kanela; Mehlhorn, Kurt; Michail, Dimitrios; Pyrga, Evangelia (2007), "Cycle bases of graphs and sampled manifolds", Computer Aided Geometric Design, 24 (8–9): 464–480, CiteSeerX 10.1.1.298.9661, doi:10.1016/j.cagd.2006.07.001, MR 2359763.

semanticscholar.org

api.semanticscholar.org

Rizzi, Romeo (2009), "Minimum weakly fundamental cycle bases are hard to find", Algorithmica, 53 (3): 402–424, doi:10.1007/s00453-007-9112-8, MR 2482112, S2CID 12675654.
Berger, Franziska; Gritzmann, Peter; de Vries, Sven (2004), "Minimum cycle bases for network graphs", Algorithmica, 40 (1): 51–62, doi:10.1007/s00453-004-1098-x, MR 2071255, S2CID 9386078.
Mehlhorn, Kurt; Michail, Dimitrios (2006), "Implementing minimum cycle basis algorithms", ACM Journal of Experimental Algorithmics, 11: 2.5, CiteSeerX 10.1.1.60.1087, doi:10.1145/1187436.1216582, S2CID 6198296.
Deo, Narsingh; Prabhu, G. M.; Krishnamoorthy, M. S. (1982), "Algorithms for generating fundamental cycles in a graph", ACM Transactions on Mathematical Software, 8 (1): 26–42, doi:10.1145/355984.355988, MR 0661120, S2CID 2260051.
Borradaile, Glencora; Eppstein, David; Nayyeri, Amir; Wulff-Nilsen, Christian (2016), "All-pairs minimum cuts in near-linear time for surface-embedded graphs", Proc. 32nd Int. Symp. Computational Geometry, Leibniz International Proceedings in Informatics (LIPIcs), vol. 51, Schloss Dagstuhl, pp. 22:1–22:16, arXiv:1411.7055, doi:10.4230/LIPIcs.SoCG.2016.22, S2CID 215762172.
Boulinier, Christian; Petit, Franck; Villain, Vincent (2004), "When graph theory helps self-stabilization", Proceedings of the Twenty-Third Annual ACM Symposium on Principles of Distributed Computing (PODC '04), New York, NY, USA: ACM, pp. 150–159, CiteSeerX 10.1.1.79.2190, doi:10.1145/1011767.1011790, ISBN 978-1581138023, S2CID 14936510.