Tight Bounds on The Clique Chromatic Number
Tight Bounds on The Clique Chromatic Number
复制标题
团色数的严格界限
DOI：
--
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发表时间：
2020
影响因子：
0.7
通讯作者：
M. Smid
中科院分区：
文献类型：
--
作者：
G. Joret;Piotr Micek;B. Reed;M. Smid
图的团色数是给图的顶点着色所需的最小色数，使得不是孤立顶点的包含式最大团都不是单色的。我们证明了每个最大度图$Delta$都有团色数$OLeft(Frc{Delta}{log~Delta}
夜)$。作为推论，我们得到了每个$n$-顶点图都有团色数$OLeft(Sqrt{frac{n}{log~n}}
夜)$。这两个结果都很紧张。
The clique chromatic number of a graph is the minimum number of colours needed to colour its vertices so that no inclusion-wise maximal clique which is not an isolated vertex is monochromatic. We show that every graph of maximum degree $Delta$ has clique chromatic number $Oleft(frac{Delta}{log~Delta}
ight)$. We obtain as a corollary that every $n$-vertex graph has clique chromatic number $Oleft(sqrt{frac{n}{log ~n}}
ight)$. Both these results are tight.