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Published in:
2012 | OriginalPaper | Chapter
Total Coloring of Planar Graphs with Maximum Degree Six
Author : Xiaodong Li
Published in: Recent Advances in Computer Science and Information Engineering
Publisher: Springer Berlin Heidelberg
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The minimum number of colors needed to properly color the vertices and edges of a graph
G
is called the total chromatic number of
G
and denoted by
χ
”(G). In this paper, the some known results are strengthen and prove that if
G
is a planar graph with maximum degree six, and for each vertex
v
, there is an integer
k
v
∈ {3,4,5,6} such that
G
has no
k
v
-cycle which contains v, then
χ
”(
G
) ≤ 8.