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Article

# Acyclic Chromatic Index of 1-Planar Graphs

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School of Mathematics and Information Science, Weifang University, Weifang 261061, China
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School of Management, Beijing University of Chinese Medicine, Beijing 100029, China
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Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China
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School of Mathematics and Computer Science, Jiangxi Science and Technology Normal University, Nanchang 330038, China
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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; https://doi.org/10.3390/math10152787
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 ${\chi }_{a}^{\prime }\left(G\right)$ 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 ${\chi }_{a}^{\prime }\left(G\right)\le \Delta +36$, where $\Delta$ denotes the maximum degree of G. This strengthens a result that if G is a triangle-free 1-planar graph, then ${\chi }_{a}^{\prime }\left(G\right)\le \Delta +16$. View Full-Text
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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. https://doi.org/10.3390/math10152787

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. https://doi.org/10.3390/math10152787

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. https://doi.org/10.3390/math10152787

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