A New Lower Bound on the Number of Edges in Colour-Critical Graphs
نویسنده
چکیده
A graph G is called k-critical if it has chromatic number k, but every proper subgraph of it is (k ? 1){colourable. We prove that every k{critical graph (k 6) on n k + 2 vertices has at least 1 2 (k?1+ k?3 (k?c)(k?1)+k?3)n edges where c = (k?5)(1 2 ? 1 (k?1)(k?2)). This improves earlier bounds established by Gallai 9] and, more recently, by Krivelevich 17].
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تاریخ انتشار 1997