最大度为3的符号图的全染色
Total Coloring of Signed Graphs with Maximum Degree 3
DOI: 10.12677/AAM.2020.910195, PDF,   
作者: 王 超：浙江师范大学，数学与计算机科学学院，浙江 金华
关键词: 符号图；全染色；最大度；Signed Graph； Total Coloring； Maximum Degree
摘要: 在图G=(V,E)中，使得相邻和相关联的元素均染不同颜色的染色方法，称为图G的正常全染色。使得G为正常全染色的最少颜色数，称为G的全色数，记为XT(Γ)。在本文中，我们给出全染色在符号图中的定义，并在最大度为3的符号图中证明了全色数的上界为5。
Abstract: For graph G=(V,E), a proper total coloring is a coloring of V and E such that no two adjacent or incident elements get the same color. The total chromatic number of G, denoted by XT(Γ), is the smallest integer k such that G have a proper total coloring. In this paper, we give a definition of total coloring in signed graphs, and prove the total chromatic number is 5 in signed graph with maximum degree 3.
文章引用：王超. 最大度为3的符号图的全染色[J]. 应用数学进展, 2020, 9(10): 1686-1692. https://doi.org/10.12677/AAM.2020.910195

参考文献

[1] Behzad, M. (1965) Graphs and Their Chromatic Numbers. Ph.D. Thesis, Michigan State University, Michigan.
[2] Vijayaditya, N. (1971) On Total Chromatic Number of a Graph. Journal of the London Mathematical Society, s2-3, 405-408. [Google Scholar] [CrossRef] 
[3] Kostochka, A.V. (1996) The Total Chromatic Number of Any Multigraph with Maximum Degree Five Is at Most Seven. Discrete Mathematics, 162, 199-214. [Google Scholar] [CrossRef] 
[4] Harary, F. (1953) On the Notion of Balance of a Signed Graph. The Michigan Mathematical Journal, 2, 143-146. [Google Scholar] [CrossRef] 
[5] Behzad, M., Chartrand, G. and Lesniak-Foster, L. (1979) Graphs and Digraphs, Wadsworth International.

为你推荐