## 特殊图形的全染色研究+文献综述

The Total Coloring of Particular Graphs
Abstract:    Vizing and Behazd posed independently the following famous conjecture, which is known as the total coloring conjecture (TCC): every simple graph with maximum degree ,  . Regarding to the total coloring of graphs, many conclusions have been acquired. Especially for some particular graphs, the total coloring conjecture is well confirmed. With the development of applying the total coloring theory in distribution of wireless, the coloring of graphs became one hot issue of graph theory. The coloring is generally pided into edge coloring, vertex coloring, total coloring and other specific coloring. In this paper, we discussed the total coloring of some particular graphs, such simple graphs as path( ) , cycle( ) and star( ), complete graph( ), complete bipartite graph . We use enumeration method to the simple graph and a total coloring matrix method to the complete graph and complete bipartite graph.
Keywords: total coloring; complete graph; complete bipartite graph

1 绪    论    1
1.1 国内外研究现状与发展趋势    1
1.2 基本符号    2
1.3 基本概念    3
2.几类特殊图形的全染色    5
2.1 路、圈、星的全染色    5
2.1.1 路的全染色    5
2.1.2 圈的全染色    6
2.1.3 星的全染色    8
2.2 完全图的全染色    10
2.2.1 完全图全染色的举例    10
2.2.2 完全图全染色的矩阵构造法    12
2.3 完全二部图的全染色    17
2.3.1 完全二部图全染色的举例    17
2.3.2 完全二部图的全染色矩阵法    18
3 致    谢    21
4 参考文献    22
1 绪    论

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