Acyclic Edge Coloring of Triangle-free 1-planar Graphs

Acyclic Edge Coloring of Triangle-free 1-planar Graphs

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...

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Veröffentlicht in:Acta mathematica Sinica. English series 2015-10, Vol.31 (10), p.1563-1570
Hauptverfasser: Song, Wen Yao, Miao, Lian Ying
Format: Artikel
Sprache:eng
Schlagworte:
Algorithms
Coloring
Critical path
Graph theory
Graphs
Mathematical models
Mathematics
Mathematics and Statistics
Planes
Studies
Theorems
三角形
图着色
平面图
无环
着色数
自由
色指数
边染色
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Beschreibung
Zusammenfassung: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.
ISSN:1439-8516
1439-7617
DOI:10.1007/s10114-015-4479-y