Author:
Yang Wanshun,Wang Yiqiao,Wang Weifan,Liu Juan,Finbow Stephen,Wang Ping
Abstract
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.
Subject
General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)
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