Acyclic Edge Coloring of 1-planar Graphs without 4-cycles  

作　　者：Wei-fan Wang Yi-qiao Wang Wan-shun Yang 

机构地区：[1]Department of Mathematics,Zhejiang Normal University,Jinhua,321004,China [2]School of Management,Beijing University of Chinese Medicine,Beijing,100029,China [3]School of Mathematics and Information Science,Weifang University,Weifang,261061,China

出　　处：《Acta Mathematicae Applicatae Sinica》2024年第1期35-44,共10页应用数学学报（英文版）

基　　金：Research supported by the National Natural Science Foundation of China (No.12031018);Research supported by the National Natural Science Foundation of China (No.12071048);Research supported by the National Natural Science Foundation of China(No.12071351);Science and Technology Commission of Shanghai Municipality (No.18dz2271000);Doctoral Scientific Research Foundation of Weifang University (No.2021BS01);Natural Science Foundation of Shandong Province (No.ZR2022MA060)。

摘　　要：An acyclic edge coloring of a graph G is a proper edge coloring such that there are no bichromatic cycles in G.The acyclic chromatic index χ'α(G) of G is the smallest k such that G has an acyclic edge coloring using k colors.It was conjectured that every simple graph G with maximum degree Δ has χ'_α(G) ≤Δ+2.A1-planar graph is a graph that can be drawn in the plane so that each edge is crossed by at most one other edge.In this paper,we show that every 1-planar graph G without 4-cycles has χ'_α(G)≤Δ+22.

关 键 词：1-planar graph acyclic edge coloring acyclic chromatic index 

分 类 号：O157.5[理学—数学]