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A note on a Brooks’ type theorem for DP-coloring. (English) Zbl 1419.05076

From a multigraph \(G\) and an integer \(t\) we obtain the multigraph \(G^t\) by replacing each edge with a set of \(t\) multiples edges. We omit the definition of a DP-coloring and of the DP-chromatic number \(\chi_{\mathrm{DP}}(G)\) of \(G\) because of space constrains.
The authors expand the following theorem of A. Yu. Bernshteyn et al. [Sib. Math. J. 58, No. 1, 28–36 (2017; Zbl 1366.05038); translation from Sib. Mat. Zh. 58, No. 1, 36–47 (2017)] of Brooks type about DP-coloring:
A connected multigraph \(G\) is not degree DP-colorable if and only if each block of \(G\) is \(K_n^t\) or \(C_n^t\) for some \(n\) and \(t\).
The direction of the mentioned expansion is in additional conditions on \(n\) and \(t\).

MSC:

05C15 Coloring of graphs and hypergraphs

Keywords:

DP-coloring

Citations:

Zbl 1366.05038
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