发表机构
Guangzhou University; Peking University（广州大学; 北京大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文改进了平面图全染色结果，证明最大度为6且不含某些特殊4环的平面图是7-全可染的，推进了全染色猜想在平面图上的研究。
AI 中文摘要
全染色猜想（TCC）是由Behzad和Vizing独立提出的一个具有挑战性的未解决问题，它断言每个简单图$G$都允许一个($\Delta(G)$+2)-全染色，其中$\Delta(G)$表示$G$的最大度。该猜想对于最大度$\Delta(G)\leq 5$的图已被证实。然而，对于平面图，唯一未解决的情况是$\Delta(G)=6$。已知最大度为6且不含4环的平面图是7-全可染的。在本文中，我们改进了这一结果，证明了任何最大度为6且不含某些特殊4环的平面图$G$是7-全可染的。
英文摘要
The Total Coloring Conjecture (TCC) is a challenging unsolved problem posed by Behzad and Vizing independently, which states that every simple graph $G$ admits a ($Δ(G)$ +2)-total-coloring, where $Δ(G)$ denotes the maximum degree of $G$. This conjecture has been confirmed for graphs with $Δ(G)\leq 5$. However, for planar graphs, the only open case is $Δ(G)=6$. It was known that planar graphs with maximum degree 6 and without 4-cycles are 7-totally-colorable. In this paper, we improve this result by showing that any planar graph $G$ of maximum degree 6, which does not contain some special 4-cycles, is 7-totally-colorable.
Comments9 pages, 7 figures
