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acyclic edge coloring of Triangle-free 1-planar Graphs

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Acta Mathematica Sinica,English Series 2015年第10期31卷 1563-1570页

作者： Wen Yao SONG Lian Ying MIAO Institute of Mathematics China University of Mining and TechnologyXuzhou

A proper edge coloring of a graph G is acyclic if there is no 2-colored cycle in G. The acyclic chromatic index of G, denoted by X＇a（G）, is the least number of colors such that G has an acyclic edge coloring. A graph is 1-planar if it can be drawn on the plane so that each edge is crossed by at most one other edge. In this paper, it is proved that X＇a（G） ≤△ A（G）＋ 22, if G is a triangle-free 1-planar graph.

关键词： acyclic chromatic index acyclic edge coloring 1-planar graph

acyclic edge coloring of IC-planar Graphs

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Acta Mathematicae Applicatae Sinica 2020年第3期36卷 581-589页

作者： Wen-yao SONG Yuan-yuan DUAN Juan WANG Lian-ying MIAO School of Mathematics and Statistics Zaozhuang UniversityZaozhuang 277160China School of Mathematics China University of Mining and TechnologyXuzhou 221116China

A proper edge coloring of a graph G is acyclic if there is no 2-colored cycle in G.The acyclic chromatic index of G is the least number of colors such that G has an acyclic edge coloring and denoted byχ′a(G).An IC-plane graph is a topological graph where every edge is crossed at most once and no two crossed edges share a vertex.In this paper,it is proved thatχ′a(G)≤Δ(G)+10,if G is an IC-planar graph without adjacent triangles andχ′a(G)≤Δ(G)+8,if G is a triangle-free IC-planar graph.

关键词： acyclic chromatic index acyclic edge coloring IC-planar graph

acyclic edge coloring of Planar Graphs without Adjacent Triangles

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Journal of Mathematical Research with Applications 2012年第4期32卷 407-414页

作者： Dezheng XIE 1,,Yanqing WU 1,2 1.College of Mathematics and Statistics,Chongqing University,Chongqing 401331,P.R.China 2.School of Mathematics and Computer Science,Shanxi Normal University,Shanxi 041000,P.R.China College of Mathematics and Statistics Chongqing University Chongqing 401331

An acyclic edge coloring of a graph G is a proper edge coloring such that there are no bichromatic cycles.The acyclic edge chromatic number of a graph G is the minimum number k such that there exists an acyclic edge coloring using k colors and is denoted by χ' a(G).In this paper we prove that χ ' a(G) ≤(G) + 5 for planar graphs G without adjacent triangles.

关键词： acyclic edge coloring acyclic edge chromatic number planar graph.

Improved Upper Bounds on acyclic edge colorings

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Acta Mathematicae Applicatae Sinica 2014年第2期30卷 305-308页

作者： Yu-wen WU Gui-ying YAN School of Information Beijing Wuzi University Academy of Mathematics and Systems Science Chinese Academy of Sciences

An acyclic edge coloring of a graph is a proper edge coloring such that every cycle contains edges of at least three distinct colors. The acyclic chromatic index of a graph G, denoted by a＇（G）, is the minimum number k such that there is an acyclic edge coloring using k colors. It is known that a＇（G） ≤ 16△ for every graph G where △denotes the maximum degree of G. We prove that a＇（G）〈 13.8A for an arbitrary graph G. We also reduce the upper bounds of a＇（G） to 9.8△ and 9△ with girth 5 and 7, respectively.

关键词： graph coloring acyclic edge coloring Lovasz local lemma