Sufficient Conditions of 6-Cycles Make Planar Graphs DP-4-Colorable

Kittikorn Nakprasit, Watcharintorn Ruksasakchai and Pongpat Sittitrai
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Kittikorn Nakprasit: Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand
Watcharintorn Ruksasakchai: Department of Mathematics, Statistics and Computer Science, Faculty of Liberal Arts and Science, Kasetsart University, Kamphaeng Saen Campus, Nakhon Pathom 73140, Thailand
Pongpat Sittitrai: Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand

Mathematics, 2022, vol. 10, issue 15, 1-13

Abstract: In simple graphs, DP-coloring is a generalization of list coloring and thus many results of DP-coloring generalize those of list coloring. Xu and Wu proved that every planar graph without 5-cycles adjacent simultaneously to 3-cycles and 4-cycles is 4-choosable. Later, Sittitrai and Nakprasit showed that if a planar graph has no pairwise adjacent 3-, 4-, and 5-cycles, then it is DP-4-colorable, which is a generalization of the result of Xu and Wu. In this paper, we extend the results on 3-, 4-, 5-, and 6-cycles by showing that every planar graph without 6-cycles simultaneously adjacent to 3-cycles, 4-cycles, and 5-cycles is DP-4-colorable, which is also a generalization of previous studies as follows: every planar graph G is DP-4-colorable if G has no 6-cycles adjacent to i -cycles where i ∈ { 3 , 4 , 5 } .

Keywords: DP-coloring; list coloring; planar graph; cycle (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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