Tight Bounds on the Clique Chromatic Number
Keyword(s):
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 $O\left(\frac{\Delta}{\log~\Delta}\right)$. We obtain as a corollary that every $n$-vertex graph has clique chromatic number $O\left(\sqrt{\frac{n}{\log ~n}}\right)$. Both these results are tight.
2018 ◽
Vol 10
(02)
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pp. 1850018
Keyword(s):
2019 ◽
Vol 11
(01)
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pp. 1950014
Keyword(s):
Keyword(s):
1997 ◽
Vol 6
(2)
◽
pp. 153-157
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