
arXiv: 1803.09141
DP-coloring (also called correspondence coloring) is a generalization of list coloring recently introduced by Dvo����k and Postle. Several known bounds for the list chromatic number of a graph $G$, $��_\ell(G)$, also hold for the DP-chromatic number of $G$, $��_{DP}(G)$. On the other hand, there are several properties of the DP-chromatic number that shows that it differs with the list chromatic number. In this note we show one such property. It is well known that $��_\ell (K_{k,t}) = k+1$ if and only if $t \geq k^k$. We show that $��_{DP} (K_{k,t}) = k+1$ if $t \geq 1 + (k^k/k!)(\log(k!)+1)$, and we show that $��_{DP} (K_{k,t}) < k+1$ if $t < k^k/k!$.
6 pages
list coloring, 05C15, 05C69, Coloring of graphs and hypergraphs, DP-coloring, graph coloring, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO)
list coloring, 05C15, 05C69, Coloring of graphs and hypergraphs, DP-coloring, graph coloring, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO)
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