Acyclic Total Colorings of Planar Graphs without l Cycles

A proper total coloring of a graph G such that there are at least 4 colors on those vertices and edges incident with a cycle of G, is called acyclic total coloring. The acyclic total chromatic number of G is the least number of colors in an acyclic total coloring of G. In this paper, it is proved th...

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Bibliographic Details
Published inActa mathematica Sinica. English series Vol. 27; no. 7; pp. 1315 - 1322
Main Authors Sun, Xiang Yong, Wu, Jian Liang
Format Journal Article
LanguageEnglish
Published Heidelberg Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 01.07.2011
Springer Nature B.V
Subjects
Coloring
Graph theory
Graphs
Mathematical analysis
Mathematics
Mathematics and Statistics
Studies
全染色
总平面图
无环
染色数
非周期性
非循环
顶点
颜色
O5C15
planar graph
cycle
Acyclic total coloring
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Summary:A proper total coloring of a graph G such that there are at least 4 colors on those vertices and edges incident with a cycle of G, is called acyclic total coloring. The acyclic total chromatic number of G is the least number of colors in an acyclic total coloring of G. In this paper, it is proved that the acyclic total chromatic number of a planar graph G of maximum degree at least k and without 1 cycles is at most △（G） ＋ 2 if （k, l） ∈ {（6, 3）, （7, 4）, （6, 5）, （7, 6）}.
Bibliography:11-2039/O1
Acyclic total coloring, cycle, planar graph
A proper total coloring of a graph G such that there are at least 4 colors on those vertices and edges incident with a cycle of G, is called acyclic total coloring. The acyclic total chromatic number of G is the least number of colors in an acyclic total coloring of G. In this paper, it is proved that the acyclic total chromatic number of a planar graph G of maximum degree at least k and without 1 cycles is at most △（G） ＋ 2 if （k, l） ∈ {（6, 3）, （7, 4）, （6, 5）, （7, 6）}.
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ISSN:1439-8516
1439-7617
DOI:10.1007/s10114-011-8640-y