Proper conflict-free 6-coloring of planar graphs without short cycles

IF 3.5 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation Pub Date : 2025-03-17 DOI:10.1016/j.amc.2025.129405

Yunlong Wang, Weifan Wang, Runrun Liu

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引用次数: 0

Abstract

A proper conflict-free l-coloring of a graph G is a proper l-coloring satisfying that for any non-isolated vertex

v \in V (G)

, there exists a color appearing exactly once in

N_{G} (v)

. The proper conflict-free chromatic number, denoted by

χ_{p c f} (G)

, is the minimal integer l so that G admits a proper conflict-free l-coloring. This notion was proposed by Fabrici et al. in 2022. They focus mainly on proper conflict-free coloring of outerplanar graphs and planar graphs. They constructed a planar graph that has no proper conflict-free 5-coloring and conjectured every planar graph G has

χ_{p c f} (G) \leq 6

. In this paper, we confirm this conjecture for planar graphs without cycles of lengths 3, 5 or 6.

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来源期刊

Applied Mathematics and Computation 数学-应用数学

CiteScore

7.90

自引率

10.00%

发文量

755

审稿时长

36 days

期刊介绍： Applied Mathematics and Computation addresses work at the interface between applied mathematics, numerical computation, and applications of systems – oriented ideas to the physical, biological, social, and behavioral sciences, and emphasizes papers of a computational nature focusing on new algorithms, their analysis and numerical results. In addition to presenting research papers, Applied Mathematics and Computation publishes review articles and single–topics issues.