Kim, Seog-Jin; Ozeki, Kenta A note on a Brooks’ type theorem for DP-coloring. (English) Zbl 1419.05076 J. Graph Theory 91, No. 2, 148-161 (2019). 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 \(t\). Reviewer: Iztok Peterin (Maribor) Cited in 19 Documents MSC: 05C15 Coloring of graphs and hypergraphs Keywords:DP-coloring Citations:Zbl 1366.05038 PDFBibTeX XMLCite \textit{S.-J. Kim} and \textit{K. Ozeki}, J. Graph Theory 91, No. 2, 148--161 (2019; Zbl 1419.05076) Full Text: DOI arXiv