Acyclic Chromatic Index of 1-Planar Graphs

Wanshun Yang, Yiqiao Wang, Weifan Wang (), Juan Liu, Stephen Finbow and Ping Wang
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Wanshun Yang: School of Mathematics and Information Science, Weifang University, Weifang 261061, China
Yiqiao Wang: School of Management, Beijing University of Chinese Medicine, Beijing 100029, China
Weifan Wang: Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China
Juan Liu: School of Mathematics and Computer Science, Jiangxi Science and Technology Normal University, Nanchang 330038, China
Stephen Finbow: Department of Mathematics and Statistics, St. Francis Xavier University, Antigonish, NS B2G 2W5, Canada
Ping Wang: Department of Mathematics and Statistics, St. Francis Xavier University, Antigonish, NS B2G 2W5, Canada

Mathematics, 2022, vol. 10, issue 15, 1-13

Abstract: The acyclic chromatic index χ a ′ ( G ) of a graph G is the smallest k for which G is a proper edge colorable using k colors. A 1-planar graph is a graph that can be drawn in plane such that every edge is crossed by at most one other edge. In this paper, we prove that every 1-planar graph G has χ a ′ ( G ) ≤ Δ + 36 , where Δ denotes the maximum degree of G . This strengthens a result that if G is a triangle-free 1-planar graph, then χ a ′ ( G ) ≤ Δ + 16 .

Keywords: 1-planar graph; acyclic edge coloring; acyclic chromatic index; discharging (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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