Abstract
We provide a certifying algorithm for the problem of deciding whether a P 5-free graph is 3-colorable by showing there are exactly six finite graphs that are P 5-free and not 3-colorable and minimal with respect to this property.
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References
Bacsó, G., Tuza, Z.: Dominating cliques in P 5-free graphs. Period. Math. Hungar. 21(4), 303–308 (1990)
Coppersmith, D., Winograd, S.: Matrix multiplication via arithmetic progressions. Journal of Symbolic Computation 9(3), 251–280 (1990)
Chudnovsky, M., Robertson, N., Seymour, P., Thomas, R.: The strong perfect graph theorem. Annals of Mathematics 164(1), 51–229 (2006)
Hoàng, C.T., Kaminśki, M., Lozin, V., Sawada, J., Shu, X.: Deciding k-colorability of P5-free graphs in polynomial time. To appear in Algorithmica
Hoàng, C.T., Kaminśki, M., Lozin, V., Sawada, J., Shu, X.: A Note on k-Colorability of P5-Free Graphs. In: Ochmański, E., Tyszkiewicz, J. (eds.) MFCS 2008. LNCS, vol. 5162, pp. 387–394. Springer, Heidelberg (2008)
Korobitsyn, D.V.: On the complexity of determining the domination number in monogenic classes of graphs. Diskret. Mat. 2(3), 90–96 (1990) (in Russian); Translation in Discrete Mathematics and Applications 2(2), 191-199 (1992)
Kral, D., Kratochvil, J., Tuza, Z., Woeginger, G.J.: Complexity of coloring graphs without forbidden induced subgraphs. In: Brandstädt, A., Le, V.B. (eds.) WG 2001. LNCS, vol. 2204, pp. 254–262. Springer, Heidelberg (2001)
Kratsch, D., McConnell, R.M., Mehlhorn, K., Spinrad, J.P.: Certifying algorithms for recognizing interval graphs and permutation graphs. SIAM J. Comput. 36(2), 326–353 (2006)
Bang Le, V., Randerath, B., Schiermeyer, I.: On the complexity of 4-coloring graphs without long induced paths. Theoretical Computer Science 389, 330–335 (2007)
Mellin, S.: Polynomielle Färbungsalgorithmen für P k -freie Graphen, Diplomarbeit am Institut für Informatik, Universität zu Köln (2002)
Randerath, B., Schiermeyer, I.: Vertex coloring and forbidden subgraphs – a survey. Graphs and Combinatorics 20(1), 1–40 (2004)
Randerath, B., Schiermeyer, I.: 3-colorability \(\in \mathcal{P}\) for P 6-free graphs. Discrete Applied Mathematics 136, 299–313 (2004)
Woeginger, G.J., Sgall, J.: The complexity of coloring graphs without long induced paths. Acta Cybernetica 15(1), 107–117 (2001)
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Bruce, D., Hoàng, C.T., Sawada, J. (2009). A Certifying Algorithm for 3-Colorability of P 5-Free Graphs. In: Dong, Y., Du, DZ., Ibarra, O. (eds) Algorithms and Computation. ISAAC 2009. Lecture Notes in Computer Science, vol 5878. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10631-6_61
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DOI: https://doi.org/10.1007/978-3-642-10631-6_61
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-10630-9
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