论文标题
具有任意连通性和色数的常见图
Common graphs with arbitrary connectivity and chromatic number
论文作者
论文摘要
图形$ h $是常见的，如果在2 edge颜色的完整图$ k_n $中的单色副本数量是$ h $的，则随机着色渐近地最小化。我们证明，给定$ k，r> 0 $，存在一个$ k $连接的公共图，带有色度至少$ r $。结果建立在最近的Kráľ，Volec和Wei的突破之上，他们获得了任意较大的色数并回答其问题的常见图。
A graph $H$ is common if the number of monochromatic copies of $H$ in a 2-edge-colouring of the complete graph $K_n$ is asymptotically minimised by the random colouring. We prove that, given $k,r>0$, there exists a $k$-connected common graph with chromatic number at least $r$. The result is built upon the recent breakthrough of Kráľ, Volec, and Wei who obtained common graphs with arbitrarily large chromatic number and answers a question of theirs.
