Part of the Lecture Notes in Computer Science book series (LNCS, volume 1380)
Colouring graphs whose chromatic number is almost their maximum degree
We present efficient algorithms for determining if the chromatic number of an input graph is close to δ. Our results are obtained via the probabilistic method.
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- 1.N. Alon and J. Spencer, The Probabilistic Method. Wiley (1992).Google Scholar
- 4.T. Emden-Weinert, S. Hougardy, and B. Kreuter, Uniquely colourable graphs and the hardness of colouring graphs with large girth, Probability, Combinatorics, and Computing, to appear.Google Scholar
- 5.P. Erdós and L. Lovász, Problems and results on 3-chromatic hypergraphs and some related questions, in: “Infinite and Finite Sets” (A. Hajnal et. al. Eds), Colloq. Math. Soc. J. Bolyai 11, North Holland, Amsterdam, 1975, 609–627.Google Scholar
- 6.R. Karp, Reducibility among combinatorial problems, In Complexity of Computer Computations, Plenum Press (1972), 85–103.Google Scholar
- 8.M. Molloy and B. Reed, A bound on the strong chromatic index of a graph, Journal of Combinatorial Theory (B), to appear.Google Scholar
- 9.M. Molloy and B. Reed, A bound on the total chromatic number, submitted.Google Scholar
- 10.M. Molloy and B. Reed, Assymptotically better list colourings, manuscript.Google Scholar
- 11.M. Molloy and B. Reed, An algorithmic version of the Lovasz Local Lemma, in preparation.Google Scholar
- 12.M. Molloy and B. Reed, Graph Colouring via the Probabilistic Method, to appear in a book edited by A. Gyarfas and L. Lovasz.Google Scholar
- 13.B. Reed, χ, δ and Ω, Journal of Graph Theory, to appear.Google Scholar
- 14.B. Reed, A strengthening of Brook's Theorem, in preparation.Google Scholar
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