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DP-colorings of graphs with high chromatic number. (English) Zbl 1369.05065
Summary: DP-coloring is a generalization of list coloring introduced recently by Z. Dvořák and L. Postle [“Correspondence coloring and its application to list-coloring planar graphs without cycles of lengths 4 to 8”, Preprint, arXiv:1508.03437]. We prove that for every $$n$$-vertex graph $$G$$ whose chromatic number $$\chi(G)$$ is “close” to $$n$$, the DP-chromatic number of $$G$$ equals $$\chi(G)$$. “Close” here means $$\chi(G) \geq n-O(\sqrt{n})$$, and we also show that this lower bound is best possible (up to the constant factor in front of $$\sqrt{n}$$), in contrast to the case of list coloring.

##### MSC:
 05C15 Coloring of graphs and hypergraphs
##### Keywords:
list coloring; DP-chromatic number
Full Text:
##### References:
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