《山东大学学报(理学版)》 ›› 2021, Vol. 56 ›› Issue (11): 71-75.doi: 10.6040/j.issn.1671-9352.0.2020.358
• • 上一篇
谭香
TAN Xiang
摘要: 设G是最大度Δ≥6且不含5-圈的平面图,若G的最大度点不关联8-圈,则有χ″(G)=Δ+1。
中图分类号:
[1] BONDY J A, MURTY U S R. Networks[M] //Graph Theory with Applications. London: Macmillan Education UK, 1976: 191-211. [2] BEHZAD M. Graphs and their chromatic numbers[D]. Michigan: Michigan State University, 1965. [3] VIZING V G. Some unsolved problems in graph theory[J]. Russian Mathematical Surveys, 1968, 23(6):125-141. [4] VIJAYADITYA N. On total chromatic number of a graph[J]. Journal of the London Mathematical Society, 1971,(3):405-408. [5] ROSENFELD M. On the total coloring of certain graphs[J]. Israel Journal of Mathematics, 1971, 9(3):396-402. [6] KOSTOCHKA A V. Upper bounds of chromatic functions on graphs[D]. Novosibirsk:[s,L] , 1978. [7] KOSTOCHKA A V. The total chromatic number of any multigraph with maximum degree five is at most seven[J]. Discrete Mathematics, 1996, 162(1/2/3):199-214. [8] SANDERS D P, ZHAO Y. On total 9-coloring planar graphs of maximum degree seven[J]. Journal of Graph Theory, 1999, 31(1):67-73. [9] BORODIN O V, KOSTOCHKA A V, WOODALL D R. Total colorings of planar graphs with large maximum degree[J]. Journal of Graph Theory, 1997, 26(1):53-59. [10] WANG W F. Total chromatic number of planar graphs with maximum degree ten[J]. Journal of Graph Theory, 2007, 54(2):91-102. [11] KOWALIK Ł, SERENI J S, ŠKREKOVSKI R. Total-coloring of plane graphs with maximum degree nine[J]. SIAM Journal on Discrete Mathematics, 2008, 22(4):1462-1479. [12] 蔡华. 平面图的若干染色问题[D]. 济南: 山东大学, 2016. CAI Hua. Some coloring problems of planar graphs[D]. Jinan: Shandong University, 2016. [13] HOU J F, LIU B, LIU G Z, et al. Total coloring of planar graphs without 6-cycles[J]. Discrete Applied Mathematics, 2011, 159(2/3):157-163. [14] SHEN L, WANG Y Q. Planar graphs with maximum degree 7 and without 5-cycles are 8-totally-colorable[J]. Discrete Mathematics, 2010, 310(17/18):2372-2379. [15] SHEN L, WANG Y Q. On the 7 total colorability of planar graphs with maximum degree 6 and without 4-cycles[J]. Graphs and Combinatorics, 2009, 25(3):401-407. |
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