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Acyclic Chromatic Index of 1-Planar Graphs

School of Mathematics and Information Science, Weifang University, Weifang 261061, China
School of Management, Beijing University of Chinese Medicine, Beijing 100029, China
Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China
School of Mathematics and Computer Science, Jiangxi Science and Technology Normal University, Nanchang 330038, China
Department of Mathematics and Statistics, St. Francis Xavier University, Antigonish, NS B2G 2W5, Canada
Author to whom correspondence should be addressed.
Academic Editors: Janez Žerovnik and Darja Rupnik Poklukar
Mathematics 2022, 10(15), 2787;
Received: 6 July 2022 / Revised: 31 July 2022 / Accepted: 3 August 2022 / Published: 5 August 2022
(This article belongs to the Special Issue Advances in Discrete Applied Mathematics and Graph Theory - II)
The acyclic chromatic index χa(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 χa(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 χa(G)Δ+16. View Full-Text
Keywords: 1-planar graph; acyclic edge coloring; acyclic chromatic index; discharging 1-planar graph; acyclic edge coloring; acyclic chromatic index; discharging
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MDPI and ACS Style

Yang, W.; Wang, Y.; Wang, W.; Liu, J.; Finbow, S.; Wang, P. Acyclic Chromatic Index of 1-Planar Graphs. Mathematics 2022, 10, 2787.

AMA Style

Yang W, Wang Y, Wang W, Liu J, Finbow S, Wang P. Acyclic Chromatic Index of 1-Planar Graphs. Mathematics. 2022; 10(15):2787.

Chicago/Turabian Style

Yang, Wanshun, Yiqiao Wang, Weifan Wang, Juan Liu, Stephen Finbow, and Ping Wang. 2022. "Acyclic Chromatic Index of 1-Planar Graphs" Mathematics 10, no. 15: 2787.

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