Every planar graph without 4-cycles adjacent to two triangles is DP-4-colorable
Combinatorics
2018-04-25 v1
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].
Cite
@article{arxiv.1804.09031,
title = {Every planar graph without 4-cycles adjacent to two triangles is DP-4-colorable},
author = {Runrun Liu and Xiangwen Li},
journal= {arXiv preprint arXiv:1804.09031},
year = {2018}
}
Comments
8pages,0figures. arXiv admin note: text overlap with arXiv:1804.03976