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202:
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39:. More precisely, the definition may allow the graph to have induced cycles of length four, or may also disallow them: the latter is referred to as
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722:(2020), "Three-in-a-tree in near linear time", in Makarychev, Konstantin; Makarychev, Yury; Tulsiani, Madhur; Kamath, Gautam;
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Proceedings of the 52nd Annual ACM SIGACT Symposium on Theory of
Computing, STOC 2020, Chicago, IL, USA, June 22–26, 2020
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problem can be solved in polynomial time on even-hole-free graphs, or whether they are NP-complete. However the
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Chang, Hsien-Chih; Lu, Hsueh-I (January 2012), "A Faster
Algorithm to Recognize Even-Hole-Free Graphs",
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present their algorithm and assert that it runs in polynomial time without giving an explicit analysis.
54:
36:
755:
634:
Chang, Hsien-Chih; Lu, Hsueh-I (July 2015), "A Faster
Algorithm to Recognize Even-Hole-Free Graphs",
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699:
661:
643:
601:
571:
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255:-complete to determine whether a graph contains an even hole that includes a specific vertex.
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gave the first polynomial time recognition algorithm for even-hole-free graphs, which runs in
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438:
416:
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711:
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Bienstock, Dan (1991), "On the complexity of testing for odd holes and induced odd paths",
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SODA '12: Proceedings of the Twenty-Third Annual ACM-SIAM Symposium on
Discrete Algorithms
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807:
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57:), which settled a conjecture by Reed. The proof was later shown to be flawed by
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While even-hole-free graphs can be recognized in polynomial time, it is
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Decomposition of even-hole-free graphs with star cutsets and 2-joins
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Graph containing no induced cycles with an even number of nodes
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732:, Association for Computing Machinery, pp. 1279–1292,
405:(2008), "Bisimplicial vertices in even-hole-free graphs",
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can be found in even-hole-free graphs in polynomial time.
797:
Information System on Graph
Classes and their Inclusions
756:"Even-hole-free graphs still have bisimplicial vertices"
49:
demonstrated that every even-hole-free graph contains a
547:"Even-hole-free graphs part II: Recognition algorithm"
502:"Even-hole-free graphs part I: Decomposition theorem"
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time. The best currently known algorithm is given by
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53:(a vertex whose neighborhood is the union of two
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314:Chudnovsky, Kawarabayashi & Seymour (2004)
8:
684:Applicable Analysis and Discrete Mathematics
205:
767:
760:Journal of Combinatorial Theory, Series B
754:Chudnovsky, Maria; Seymour, Paul (2023),
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636:Journal of Combinatorial Theory, Series B
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349:{\displaystyle {\mathcal {O}}(n^{40})}
197:{\displaystyle {\mathcal {O}}(n^{11})}
149:{\displaystyle {\mathcal {O}}(n^{19})}
105:{\displaystyle {\mathcal {O}}(n^{40})}
316:estimate that it runs in "time about
241:{\displaystyle {\mathcal {O}}(n^{9})}
7:
14:
677:"Even-hole-free graphs: a survey"
462:(2004), "Detecting even holes",
408:Journal of Combinatorial Theory
59:Chudnovsky & Seymour (2023)
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114:da Silva & Vušković (2008)
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1:
718:Lai, Kai-Yuan; Lu, Hsueh-I;
444:10.1016/0012-365X(91)90098-M
61:, who gave a correct proof.
617:10.1137/1.9781611973099.101
206:Lai, Lu & Thorup (2020)
47:Addario-Berry et al. (2008)
830:
778:10.1016/j.jctb.2023.02.009
658:10.1016/j.jctb.2015.02.001
421:10.1016/j.jctb.2007.12.006
288:"even-cycle--free graphs"
792:"Even-hole-free graphs"
748:10.1145/3357713.3384235
582:da Silva, Murilo V.G.;
555:Journal of Graph Theory
510:Journal of Graph Theory
465:Journal of Graph Theory
456:Kawarabayashi, Ken-ichi
393:Addario-Berry, Louigi;
310:Conforti et al. (2002b)
264:maximum independent set
116:later improved this to
70:Conforti et al. (2002b)
35:with an even number of
696:10.2298/AADM100812027V
350:
258:It is unknown whether
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41:even-cycle-free graphs
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162:Chang & Lu (2015)
158:Chang & Lu (2012)
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107:
430:Discrete Mathematics
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292:www.graphclasses.org
212:
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120:
76:
537:Conforti, Michele;
492:Conforti, Michele;
397:; Havet, Frédéric;
51:bisimplicial vertex
673:Vušković, Kristina
584:Vušković, Kristina
543:Vušković, Kristina
539:Cornuéjols, Gérard
498:Vušković, Kristina
494:Cornuéjols, Gérard
346:
238:
194:
146:
102:
31:if it contains no
627:978-1-61197-210-8
568:10.1002/jgt.10045
523:10.1002/jgt.10006
500:(January 2002a),
478:10.1002/jgt.20040
452:Chudnovsky, Maria
395:Chudnovsky, Maria
164:improved this to
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545:(August 2002b),
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496:; Kapoor, Ajai;
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415:(6): 1119–1164,
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785:External links
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724:Chuzhoy, Julia
720:Thorup, Mikkel
715:
690:(2): 219–240,
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562:(4): 238–266,
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268:maximum clique
260:graph coloring
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208:which runs in
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29:even-hole-free
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600:: 1286–1297,
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472:(2): 85–111,
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460:Seymour, Paul
457:
453:
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403:Seymour, Paul
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33:induced cycle
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27:, a graph is
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437:(1): 85–92,
434:
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411:, Series B,
406:
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361:
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295:, retrieved
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252:
250:
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25:graph theory
21:mathematical
18:
642:: 141–161,
517:(1): 6–49,
399:Reed, Bruce
65:Recognition
769:1909.10967
739:1909.07446
387:References
297:2023-03-12
649:1311.0358
607:1311.0358
808:Category
726:(eds.),
704:43666110
675:(2010),
586:(2008),
576:15044085
531:12947855
262:and the
37:vertices
23:area of
712:2724633
666:1744497
486:2945499
55:cliques
19:In the
710:
702:
664:
624:
574:
529:
484:
248:time.
112:time.
764:arXiv
734:arXiv
700:JSTOR
680:(PDF)
662:S2CID
644:arXiv
602:arXiv
572:S2CID
550:(PDF)
527:S2CID
505:(PDF)
482:S2CID
274:Notes
622:ISBN
160:and
774:doi
744:doi
692:doi
654:doi
640:113
612:doi
564:doi
519:doi
474:doi
439:doi
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335:n
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