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Mathematics > Combinatorics

arXiv:1804.09031 (math)
[Submitted on 21 Apr 2018]

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

Authors:Runrun Liu, Xiangwen Li
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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].
Comments: 8pages,0figures. arXiv admin note: text overlap with arXiv:1804.03976
Subjects: Combinatorics (math.CO)
Cite as: arXiv:1804.09031 [math.CO]
  (or arXiv:1804.09031v1 [math.CO] for this version)
  https://doi.org/10.48550/arXiv.1804.09031

Submission history

From: Runrun Liu [view email]
[v1] Sat, 21 Apr 2018 13:56:05 UTC (8 KB)
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