Colour-critical graphs with few edges
نویسندگان
چکیده
A graph G is called k-critical if G is k-chromatic but every proper subgraph of G has chromatic number at most k 1. In this paper the following result is proved. If G is a k-critical graph (k>~4) on n vertices, then 21E(G)I>(k 1)n ÷ ((k 3)/(k 2 3))n + k 4 where n>~k + 2 and n ~ 2 k 1. This improves earlier bounds established by Dirac (1957) and Gallai (1963). (~) 1998 Elsevier Science B.V. All rights reserved
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عنوان ژورنال:
- Discrete Mathematics
دوره 191 شماره
صفحات -
تاریخ انتشار 1998