科研之友
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摘要
If n >= k + 1 and G is a connected n-vertex graph, then one can add [GRAPHICS] edges to G so that the resulting graph contains the complete graph Kk+1. This yields that for any connected graph G with at least k + 1 vertices, one can add [GRAPHICS] edges to G so that the resulting graph has chromatic number > k. A long time ago, Bollobas suggested that for every k >= 3 there exists a k-chromatic graph G(k) such that after adding to it any [GRAPHICS] - 1 edges, the chromatic number of the resulting graph is still k. In this note we prove this conjecture.
- 出版日期2016-7
