Abstract
A graph is called t-perfect if its stable set polytope is defined by non-negativity, edge and odd-cycle inequalities. We show that it can be decided in polynomial time whether a given claw-free graph is t-perfect.
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References
Boulala, M., Uhry, J.P.: Polytope des indépendants d’un graphe série-parallèle. Disc. Math. 27, 225–243 (1979)
Bruhn, H., Stein, M.: t-perfection is always strong for claw-free graphs. SIAM. J. Discrete Math. 24, 770–781 (2010)
Bruhn, H., Stein, M.: On claw-free t-perfect graphs. Math. Program. 133, 461–480 (2012)
Chudnovsky, M., Cornuéjols, G., Liu, X., Seymour, P., Vušković, K.: Recognizing berge graphs. Combinatorica 25, 143–187 (2005)
Chudnovsky, M., Seymour, P., Robertson, N., Thomas, R.: The strong perfect graph theorem. Ann. Math. 164, 51–229 (2006)
Chvátal, V.: On certain polytopes associated with graphs. J. Combin. Theory (Series B) 18, 138–154 (1975)
Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to algorithms, 3rd edn. MIT Press (2009)
Diestel, R.: Graph theory, 4th edn. Springer (2010)
Eisenbrand, F., Funke, S., Garg, N., Könemann, J.: A combinatorial algorithm for computing a maximum independent set in a t-perfect graph. In: SODA, pp. 517–522 (2002)
Fellows, M.R., Kratochvil, J., Middendorf, M., Pfeiffer, F.: The complexity of induced minors and related problems. Algorithmica 13, 266–282 (1995)
Fonlupt, J., Uhry, J.P.: Transformations which preserve perfectness and h-perfectness of graphs. Ann. Disc. Math. 16, 83–95 (1982)
Gerards, A.M.H., Shepherd, F.B.: The graphs with all subgraphs t-perfect. SIAM J. Discrete Math. 11, 524–545 (1998)
Golovach, P.A., Paulusma, D., van Leeuwen, E.J.: Induced disjoint paths in claw-free graphs, arXiv:1202.4419v1
Huynh, T.C.T.: The linkage problem for group-labelled graphs, PhD thesis, University of Waterloo (2009)
Kawarabayashi, K., Reed, B., Wollan, P.: The graph minor algorithm with parity conditions. In: FOCS, pp. 27–36 (2011)
Király, T., Páp, J.: A note on kernels in h-perfect graphs, Tech. Report TR-2007-03, Egerváry Research Group (2007)
Király, T., Páp, J.: Kernels, stable matchings and Scarf’s Lemma, Tech. Report TR-2008-13, Egerváry Research Group (2008)
Maffray, F., Trotignon, N.: Algorithms for perfectly contractile graphs. SIAM J. Discrete Math. 19, 553–574 (2005)
Padberg, M.W.: Perfect zero-one matrices. Math. Programming 6, 180–196 (1974)
Roussopoulos, N.D.: A max {m, n } algorithm for determining the graph H from its line graph G. Inf. Process. Lett. 2, 108–112 (1973)
Sbihi, N., Uhry, J.P.: A class of h-perfect graphs. Disc. Math. 51, 191–205 (1984)
Schrijver, A.: Strong t-perfection of bad-K 4-free graphs. SIAM J. Discrete Math. 15, 403–415 (2002)
Schrijver, A.: Combinatorial optimization. In: Polyhedra and efficiency. Springer (2003)
Shepherd, F.B.: Applying Lehman’s theorems to packing problems. Math. Prog. 71, 353–367 (1995)
van ’t Hof, P., Kamiński, M., Paulusma, D.: Finding induced paths of given parity in claw-free graphs. Algorithmica 62, 537–563 (2012)
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Bruhn, H., Schaudt, O. (2014). Claw-Free t-Perfect Graphs Can Be Recognised in Polynomial Time. In: Lee, J., Vygen, J. (eds) Integer Programming and Combinatorial Optimization. IPCO 2014. Lecture Notes in Computer Science, vol 8494. Springer, Cham. https://doi.org/10.1007/978-3-319-07557-0_34
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DOI: https://doi.org/10.1007/978-3-319-07557-0_34
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