首页|The acyclic chromatic index of planar graphs without 4-,6-cycles and intersecting triangles
The acyclic chromatic index of planar graphs without 4-,6-cycles and intersecting triangles
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A proper edge k-coloring is a mapping φ:E(G)→ {1,2,…,k} such that any two adjacent edges receive different colors.A proper edge k-coloring φ of G is called acyclic if there are no bichromatic cycles in G.The acyclic chromatic index of G,denoted by x'a(G),is the smallest integer k such that G is acyclically edge k-colorable.In this paper,we show that if G is a plane graph without 4-,6-cycles and intersecting 3-cycles,Δ(G)≥ 9,then x'a(G)≤Δ(G)+1.
Acyclic edge coloringplane graphcycle
Yuehua BU、Qi JIA、Hongguo ZHU
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College of Mathematics and Computer Science,Zhejiang Normal University,Jinhua 321004,China
Xingzhi College,Zhejiang Normal University,Jinhua 321004,China
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