Every planar graph without 4-cycles adjacent to two triangles is DP-4-colorable

TL;DR

This paper proves that certain planar graphs lacking specific cycle configurations are DP-4-colorable, advancing understanding of graph coloring properties and extending previous results in the field.

Contribution

It establishes that planar graphs without 4-cycles adjacent to two triangles are DP-4-colorable, improving prior bounds and conjectures in graph coloring theory.

Findings

Proves DP-4-colorability for a new class of planar graphs

Extends previous results on 4-choosability and DP-coloring

Provides a broader understanding of coloring constraints in planar graphs

Abstract

Wang and Lih in 2002 conjectured that every planar graph without adjacent triangles is 4-choosable. In this paper, we prove that every planar graph without any 4-cycle adjacent to two triangles is DP-4-colorable, which improves the results of Lam, Xu and Liu [Journal of Combin. Theory, Ser. B, 76 (1999) 117--126], of Cheng, Chen and Wang [Discrete Math., 339(2016) 3052--3057] and of Kim and Yu [arXiv:1709.09809v1].