DP-4-Colorability on Planar Graphs Excluding 7-Cycles Adjacent to 4- or 5-Cycles

Fan Yang (), Xiangwen Li and Ziwen Huang
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Fan Yang: School of Mathematics and Science, Nanjing Tech University, Nanjing 211816, China
Xiangwen Li: School of Mathematics & Statistics, Central China Normal University, Wuhan 430079, China
Ziwen Huang: School of Mathematics and Computer Science & Center of Applied Mathematics, Yichun University, Yichun 336000, China

Mathematics, 2025, vol. 13, issue 2, 1-18

Abstract: In order to resolve Borodin’s Conjecture, DP-coloring was introduced in 2017 to extend the concept of list coloring. In previous works, it is proved that every planar graph without 7-cycles and butterflies is DP-4-colorable. And any planar graph that does not have 5-cycle adjacent to 6-cycle is DP-4-colorable. The existing research mainly focus on the forbidden adjacent cycles that guarantee the DP-4-colorability for planar graph. In this paper, we demonstrate that any planar graph G that excludes 7-cycles adjacent to k -cycles (for each k = 4 , 5 ), and does not feature a Near-bow-tie as an induced subgraph, is DP-4-colorable. This result extends the findings of the previous works mentioned above.

Keywords: planar graph; DP-4-colorable; list coloring (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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