References analysis of the Wikipedia article "Pathwidth" in the English version

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Diestel & Kühn (2005). Diestel, Reinhard; Kühn, Daniela (2005), "Graph minor hierarchies", Discrete Applied Mathematics, 145 (2): 167–182, doi:10.1016/j.dam.2004.01.010.

Robertson & Seymour (1983). Robertson, Neil; Seymour, Paul (1983), "Graph minors. I. Excluding a forest", Journal of Combinatorial Theory, Series B, 35 (1): 39–61, doi:10.1016/0095-8956(83)90079-5.

Kinnersley (1989); Bodlaender (1998). Kinnersley, Nancy G. (1989), Obstruction set isolation for layout permutation problems (Ph.D. thesis), Washington State University, ProQuest 303738168; see Theorem 6.A, p. 44. Bodlaender, Hans L. (1998), "A partial k-arboretum of graphs with bounded treewidth", Theoretical Computer Science, 209 (1–2): 1–45, doi:10.1016/S0304-3975(97)00228-4.

Robertson & Seymour (2003). Robertson, Neil; Seymour, Paul (2003), "Graph minors. XVI. Excluding a non-planar graph", Journal of Combinatorial Theory, Series B, 89 (1): 43–76, doi:10.1016/S0095-8956(03)00042-X.

Kashiwabara & Fujisawa (1979); Ohtsuki et al. (1979); Lengauer (1981); Arnborg, Corneil & Proskurowski (1987). Kashiwabara, T.; Fujisawa, T. (1979), "NP-completeness of the problem of finding a minimum-clique-number interval graph containing a given graph as a subgraph", Proc. International Symposium on Circuits and Systems, pp. 657–660. Ohtsuki, Tatsuo; Mori, Hajimu; Kuh, Ernest S.; Kashiwabara, Toshinobu; Fujisawa, Toshio (1979), "One-dimensional logic gate assignment and interval graphs", IEEE Transactions on Circuits and Systems, 26 (9): 675–684, doi:10.1109/TCS.1979.1084695. Lengauer, Thomas (1981), "Black-white pebbles and graph separation", Acta Informatica, 16 (4): 465–475, doi:10.1007/BF00264496, S2CID 19415148. Arnborg, Stefan; Corneil, Derek G.; Proskurowski, Andrzej (1987), "Complexity of finding embeddings in a

k

-tree", SIAM Journal on Algebraic and Discrete Methods, 8 (2): 277–284, doi:10.1137/0608024.

Bodlaender et al. (1992). Bodlaender, Hans L.; Gilbert, John R.; Hafsteinsson, Hjálmtýr; Kloks, Ton (1992), "Approximating treewidth, pathwidth, and minimum elimination tree height", Graph-Theoretic Concepts in Computer Science, Lecture Notes in Computer Science, vol. 570, pp. 1–12, doi:10.1007/3-540-55121-2_1, hdl:1874/17927, ISBN 978-3-540-55121-8.

Bodlaender (1996); Bodlaender & Kloks (1996) Bodlaender, Hans L. (1996), "A linear-time algorithm for finding tree-decompositions of small treewidth", SIAM Journal on Computing, 25 (6): 1305–1317, doi:10.1137/S0097539793251219, hdl:1874/16670. Bodlaender, Hans L.; Kloks, Ton (1996), "Efficient and constructive algorithms for the pathwidth and treewidth of graphs", Journal of Algorithms, 21 (2): 358–402, doi:10.1006/jagm.1996.0049, hdl:1874/16538.

Möhring (1990); Scheffler (1990); Ellis, Sudborough & Turner (1994); Peng et al. (1998); Skodinis (2000); Skodinis (2003); Coudert, Huc & Mazauric (2012). Möhring, Rolf H. (1990), "Graph problems related to gate matrix layout and PLA folding", in Tinhofer, G.; Mayr, E.; Noltemeier, H.; et al. (eds.), Computational Graph Theory, Computing Supplementum, vol. 7, Springer-Verlag, pp. 17–51, ISBN 3-211-82177-5. Scheffler, Petra (1990), "A linear algorithm for the pathwidth of trees", in Bodendiek, R.; Henn, R. (eds.), Topics in Combinatorics and Graph Theory, Physica-Verlag, pp. 613–620. Ellis, J. A.; Sudborough, I. H.; Turner, J. S. (1994), "The vertex separation and search number of a tree", Information and Computation, 113 (1): 50–79, doi:10.1006/inco.1994.1064. Peng, Sheng-Lung; Ho, Chin-Wen; Hsu, Tsan-sheng; Ko, Ming-Tat; Tang, Chuan Yi (1998), "A linear-time algorithm for constructing an optimal node-search strategy of a tree", in Hsu, Wen-Lian; Kao, Ming-Yang (eds.), Computing and Combinatorics, 4th Annual International Conference, COCOON '98, Taipei, Taiwan, R.o.C., August 12–14, 1998, Proceedings, Lecture Notes in Computer Science, vol. 1449, Springer, pp. 279–288, doi:10.1007/3-540-68535-9_32, ISBN 978-3-540-64824-6 Skodinis, Konstantin (2000), "Computing optimal linear layouts of trees in linear time", Proc. 8th European Symposium on Algorithms (ESA 2000), Lecture Notes in Computer Science, vol. 1879, Springer-Verlag, pp. 403–414, doi:10.1007/3-540-45253-2_37, ISBN 978-3-540-41004-1. Skodinis, Konstantin (2003), "Construction of linear tree-layouts which are optimal with respect to vertex separation in linear time", Journal of Algorithms, 47 (1): 40–59, doi:10.1016/S0196-6774(02)00225-0. Coudert, David; Huc, Florian; Mazauric, Dorian (2012), "A Distributed Algorithm for Computing the Node Search Number in Trees" (PDF), Algorithmica, 63 (1): 158–190, doi:10.1007/s00453-011-9524-3.

Arnborg (1985). Arnborg, Stefan (1985), "Efficient algorithms for combinatorial problems on graphs with bounded decomposability – A survey", BIT, 25 (1): 2–23, doi:10.1007/BF01934985, S2CID 122263659.

Aspvall, Proskurowski & Telle (2000). Aspvall, Bengt; Proskurowski, Andrzej; Telle, Jan Arne (2000), "Memory requirements for table computations in partial k-tree algorithms", Algorithmica, 27 (3): 382–394, doi:10.1007/s004530010025, S2CID 9690525.

Bodlaender (1998), Theorem 29, p. 13. Bodlaender, Hans L. (1998), "A partial k-arboretum of graphs with bounded treewidth", Theoretical Computer Science, 209 (1–2): 1–45, doi:10.1016/S0304-3975(97)00228-4.

Kinnersley (1989); Kinnersley (1992); Bodlaender (1998), Theorem 51. Kinnersley, Nancy G. (1989), Obstruction set isolation for layout permutation problems (Ph.D. thesis), Washington State University, ProQuest 303738168; see Theorem 6.A, p. 44. Kinnersley, Nancy G. (1992), "The vertex separation number of a graph equals its path-width", Information Processing Letters, 42 (6): 345–350, doi:10.1016/0020-0190(92)90234-M. Bodlaender, Hans L. (1998), "A partial k-arboretum of graphs with bounded treewidth", Theoretical Computer Science, 209 (1–2): 1–45, doi:10.1016/S0304-3975(97)00228-4.

Korach & Solel (1993), Lemma 3 p.99; Bodlaender (1998), Theorem 47, p. 24. Korach, Ephraim; Solel, Nir (1993), "Tree-width, path-width, and cutwidth", Discrete Applied Mathematics, 43 (1): 97–101, doi:10.1016/0166-218X(93)90171-J. Bodlaender, Hans L. (1998), "A partial k-arboretum of graphs with bounded treewidth", Theoretical Computer Science, 209 (1–2): 1–45, doi:10.1016/S0304-3975(97)00228-4.

Korach & Solel (1993), Lemma 1, p. 99; Bodlaender (1998), Theorem 49, p. 24. Korach, Ephraim; Solel, Nir (1993), "Tree-width, path-width, and cutwidth", Discrete Applied Mathematics, 43 (1): 97–101, doi:10.1016/0166-218X(93)90171-J. Bodlaender, Hans L. (1998), "A partial k-arboretum of graphs with bounded treewidth", Theoretical Computer Science, 209 (1–2): 1–45, doi:10.1016/S0304-3975(97)00228-4.

Korach & Solel (1993), Theorem 5, p. 99; Bodlaender (1998), Theorem 66, p. 30. Scheffler (1992) gives a tighter upper bound of

log 3 (2 n + 1)

on the pathwidth of an

n

-vertex forest. Korach, Ephraim; Solel, Nir (1993), "Tree-width, path-width, and cutwidth", Discrete Applied Mathematics, 43 (1): 97–101, doi:10.1016/0166-218X(93)90171-J. Bodlaender, Hans L. (1998), "A partial k-arboretum of graphs with bounded treewidth", Theoretical Computer Science, 209 (1–2): 1–45, doi:10.1016/S0304-3975(97)00228-4. Scheffler, Petra (1992), "Optimal embedding of a tree into an interval graph in linear time", in Nešetřil, Jaroslav; Fiedler, Miroslav (eds.), Fourth Czechoslovakian Symposium on Combinatorics, Graphs and Complexity, Elsevier.

Korach & Solel (1993), Theorem 6, p. 100; Bodlaender (1998), Corollary 24, p.10. Korach, Ephraim; Solel, Nir (1993), "Tree-width, path-width, and cutwidth", Discrete Applied Mathematics, 43 (1): 97–101, doi:10.1016/0166-218X(93)90171-J. Bodlaender, Hans L. (1998), "A partial k-arboretum of graphs with bounded treewidth", Theoretical Computer Science, 209 (1–2): 1–45, doi:10.1016/S0304-3975(97)00228-4.

Gurski & Wanke (2007). Gurski, Frank; Wanke, Egon (2007), "Line graphs of bounded clique-width", Discrete Mathematics, 307 (22): 2734–2754, doi:10.1016/j.disc.2007.01.020.

Golovach (1993). Golovach, P. A. (1993), "The cutwidth of a graph and the vertex separation number of the line graph", Discrete Mathematics and Applications, 3 (5): 517–522, doi:10.1515/dma.1993.3.5.517, S2CID 120745961.

Bodlaender (1998), Corollary 23, p. 10. Bodlaender, Hans L. (1998), "A partial k-arboretum of graphs with bounded treewidth", Theoretical Computer Science, 209 (1–2): 1–45, doi:10.1016/S0304-3975(97)00228-4.

Bodlaender (1998), Theorem 20, p. 9. Bodlaender, Hans L. (1998), "A partial k-arboretum of graphs with bounded treewidth", Theoretical Computer Science, 209 (1–2): 1–45, doi:10.1016/S0304-3975(97)00228-4.

Bodlaender & Fomin (2002); Coudert, Huc & Sereni (2007). Bodlaender, Hans L.; Fomin, Fedor V. (2002), "Approximation of pathwidth of outerplanar graphs", Journal of Algorithms, 43 (2): 190–200, doi:10.1016/S0196-6774(02)00001-9. Coudert, David; Huc, Florian; Sereni, Jean-Sébastien (2007), "Pathwidth of outerplanar graphs" (PDF), Journal of Graph Theory, 55 (1): 27–41, doi:10.1002/jgt.20218.

Fomin & Thilikos (2007); Amini, Huc & Pérennes (2009). Fomin, Fedor V.; Thilikos, Dimitrios M. (2007), "On self duality of pathwidth in polyhedral graph embeddings", Journal of Graph Theory, 55 (1): 42–54, doi:10.1002/jgt.20219. Amini, Omid; Huc, Florian; Pérennes, Stéphane (2009), "On the path-width of planar graphs", SIAM Journal on Discrete Mathematics, 23 (3): 1311–1316, doi:10.1137/060670146.

Fomin (2003). Fomin, Fedor V. (2003), "Pathwidth of planar and line graphs", Graphs and Combinatorics, 19 (1): 91–99, doi:10.1007/s00373-002-0490-z, S2CID 43123449.

Bodlaender & Möhring (1990). Bodlaender, Hans L.; Möhring, Rolf H. (1990), "The pathwidth and treewidth of cographs", Proc. 2nd Scandinavian Workshop on Algorithm Theory, Lecture Notes in Computer Science, vol. 447, Springer-Verlag, pp. 301–309, doi:10.1007/3-540-52846-6_99, hdl:1874/16625, ISBN 978-3-540-52846-3.

Bodlaender, Kloks & Kratsch (1993). Bodlaender, Hans L.; Kloks, Ton; Kratsch, Dieter (1993), "Treewidth and pathwidth of permutation graphs", Proc. 20th International Colloquium on Automata, Languages and Programming (ICALP 1993), Lecture Notes in Computer Science, vol. 700, Springer-Verlag, pp. 114–125, doi:10.1007/3-540-56939-1_66, hdl:1874/16657, ISBN 978-3-540-56939-8.

Habib & Möhring (1994). Habib, Michel; Möhring, Rolf H. (1994), "Treewidth of cocomparability graphs and a new order-theoretic parameter", Order, 11 (1): 47–60, doi:10.1007/BF01462229, S2CID 2648030.

Garbe (1995). Garbe, Renate (1995), "Tree-width and path-width of comparability graphs of interval orders", Proc. 20th International Workshop Graph-Theoretic Concepts in Computer Science (WG'94), Lecture Notes in Computer Science, vol. 903, Springer-Verlag, pp. 26–37, doi:10.1007/3-540-59071-4_35, ISBN 978-3-540-59071-2.

Fomin & Høie (2006). Fomin, Fedor V.; Høie, Kjartan (2006), "Pathwidth of cubic graphs and exact algorithms", Information Processing Letters, 97 (5): 191–196, doi:10.1016/j.ipl.2005.10.012.

Fomin et al. (2008). Fomin, Fedor V.; Kratsch, Dieter; Todinca, Ioan; Villanger, Yngve (2008), "Exact algorithms for treewidth and minimum fill-in", SIAM Journal on Computing, 38 (3): 1058–1079, doi:10.1137/050643350, hdl:1956/1151.

Monien & Sudborough (1988). Monien, B.; Sudborough, I. H. (1988), "Min cut is NP-complete for edge weighted trees", Theoretical Computer Science, 58 (1–3): 209–229, doi:10.1016/0304-3975(88)90028-X.

Gustedt (1993). Gustedt, Jens (1993), "On the pathwidth of chordal graphs", Discrete Applied Mathematics, 45 (3): 233–248, doi:10.1016/0166-218X(93)90012-D.

Kloks, Kratsch & Müller (1995). A chordal domino is a chordal graph in which every vertex belongs to at most two maximal cliques. Kloks, Ton; Kratsch, Dieter; Müller, H. (1995), "Dominoes", Proc. 20th International Workshop Graph-Theoretic Concepts in Computer Science (WG'94), Lecture Notes in Computer Science, vol. 903, Springer-Verlag, pp. 106–120, doi:10.1007/3-540-59071-4_41, ISBN 978-3-540-59071-2.

Kloks et al. (1993). Kloks, T.; Bodlaender, H.; Müller, H.; Kratsch, D. (1993), "Computing treewidth and minimum fill-in: all you need are the minimal separators", Proc. 1st European Symposium on Algorithms (ESA'93) (Lecture Notes in Computer Science), vol. 726, Springer-Verlag, pp. 260–271, doi:10.1007/3-540-57273-2_61, ISBN 978-3-540-57273-2.

Kloks & Bodlaender (1992); Gustedt (1993). Kloks, Ton; Bodlaender, Hans L. (1992), "Approximating treewidth and pathwidth of some classes of perfect graphs", Proc. 3rd International Symposium on Algorithms and Computation (ISAAC'92), Lecture Notes in Computer Science, vol. 650, Springer-Verlag, pp. 116–125, doi:10.1007/3-540-56279-6_64, hdl:1874/16672, ISBN 978-3-540-56279-5. Gustedt, Jens (1993), "On the pathwidth of chordal graphs", Discrete Applied Mathematics, 45 (3): 233–248, doi:10.1016/0166-218X(93)90012-D.

Garbe (1995) credits this result to the 1993 Ph.D. thesis of Ton Kloks; Garbe's polynomial time algorithm for comparability graphs of interval orders generalizes this result, since any chordal graph must be a comparability graph of this type. Garbe, Renate (1995), "Tree-width and path-width of comparability graphs of interval orders", Proc. 20th International Workshop Graph-Theoretic Concepts in Computer Science (WG'94), Lecture Notes in Computer Science, vol. 903, Springer-Verlag, pp. 26–37, doi:10.1007/3-540-59071-4_35, ISBN 978-3-540-59071-2.

Suchan & Todinca (2007). Suchan, Karol; Todinca, Ioan (2007), "Pathwidth of circular-arc graphs", Proc. 33rd International Workshop on Graph-Theoretic Concepts in Computer Science (WG 2007), Lecture Notes in Computer Science, vol. 4769, Springer-Verlag, pp. 258–269, doi:10.1007/978-3-540-74839-7_25, ISBN 978-3-540-74838-0.

Feige, Hajiaghayi & Lee (2005). Feige, Uriel; Hajiaghayi, Mohammadtaghi; Lee, James R. (2005), "Improved approximation algorithms for minimum-weight vertex separators", Proc. 37th ACM Symposium on Theory of Computing (STOC 2005), pp. 563–572, doi:10.1145/1060590.1060674, ISBN 1581139608, S2CID 14097859.

Robertson & Seymour (2004). Robertson, Neil; Seymour, Paul D. (2004), "Graph Minors. XX. Wagner's conjecture", Journal of Combinatorial Theory, Series B, 92 (2): 325–357, doi:10.1016/j.jctb.2004.08.001.

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Kinnersley (1992); Takahashi, Ueno & Kajitani (1994); Bodlaender (1998), p. 8. Kinnersley, Nancy G. (1992), "The vertex separation number of a graph equals its path-width", Information Processing Letters, 42 (6): 345–350, doi:10.1016/0020-0190(92)90234-M. Takahashi, Atsushi; Ueno, Shuichi; Kajitani, Yoji (1994), "Minimal acyclic forbidden minors for the family of graphs with bounded path-width", Discrete Mathematics, 127 (1–3): 293–304, doi:10.1016/0012-365X(94)90092-2. Bodlaender, Hans L. (1998), "A partial k-arboretum of graphs with bounded treewidth", Theoretical Computer Science, 209 (1–2): 1–45, doi:10.1016/S0304-3975(97)00228-4.

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-tree", SIAM Journal on Algebraic and Discrete Methods, 8 (2): 277–284, doi:10.1137/0608024.

Fomin (2003). Fomin, Fedor V. (2003), "Pathwidth of planar and line graphs", Graphs and Combinatorics, 19 (1): 91–99, doi:10.1007/s00373-002-0490-z, S2CID 43123449.

Pathwidth (English Wikipedia)

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