A new lower bound on the number of edges in colour-critical graphs and hypergraphs
نویسندگان
چکیده
A graph G is called k-critical if it has chromatic number k; but every proper subgraph of G is ðk 1Þ-colourable. We prove that every k-critical graph ðkX6Þ on nXk þ 2 vertices has at least 1 2 ðk 1þ k 3 ðk cÞðk 1Þþk 3Þn edges where c 1⁄4 ðk 5Þð2 1 ðk 1Þðk 2ÞÞ: This improves earlier bounds established by Gallai (Acad. Sci. 8 (1963) 165) and by Krivelevich (Combinatorica 17 (1999) 401). r 2002 Elsevier Science (USA). All rights reserved.
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عنوان ژورنال:
- J. Comb. Theory, Ser. B
دوره 87 شماره
صفحات -
تاریخ انتشار 2003