A Note on the Minimum Total Coloring of Planar Graphs

Graph coloring is an important tool in the study of optimization, computer science, network design, e.g., file transferring in a computer network, pattern matching, computation of Hessians matrix and so on. In this paper, we consider one important coloring, vertex coloring of a total graph, which is...

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Bibliographic Details
Published inActa mathematica Sinica. English series Vol. 32; no. 8; pp. 967 - 974
Main Authors Wang, Hui Juan, Luo, Zhao Yang, Liu, Bin, Gu, Yan, Gao, Hong Wei
Format Journal Article
LanguageEnglish
Published Beijing Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 01.08.2016
Springer Nature B.V
Subjects
Coloring
Computation
Design optimization
Graph coloring
Graphs
Mathematical models
Mathematics
Mathematics and Statistics
Matrix
Networks
Optimization
Pattern analysis
Studies
Theorems
全染色
平面图
文件传输
注记
着色问题
网络设计
计算机科学
计算机网络
cycle
Planar graph
total coloring
05C15
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Summary:Graph coloring is an important tool in the study of optimization, computer science, network design, e.g., file transferring in a computer network, pattern matching, computation of Hessians matrix and so on. In this paper, we consider one important coloring, vertex coloring of a total graph, which is also called total coloring. We consider a planar graph G with maximum degree △（G） 〉 8, and proved that if G contains no adjacent i,j-cycles with two chords for some i,j E {5,6,7}, then G is total-（△ ＋ 1）-colorable.
Bibliography:11-2039/O1
Graph coloring is an important tool in the study of optimization, computer science, network design, e.g., file transferring in a computer network, pattern matching, computation of Hessians matrix and so on. In this paper, we consider one important coloring, vertex coloring of a total graph, which is also called total coloring. We consider a planar graph G with maximum degree △（G） 〉 8, and proved that if G contains no adjacent i,j-cycles with two chords for some i,j E {5,6,7}, then G is total-（△ ＋ 1）-colorable.
Planar graph, total coloring, cycle
ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
ISSN:1439-8516
1439-7617
DOI:10.1007/s10114-016-5427-1