在一些充分条件下的不含4圈和7圈的平面图是2-弱退化的  

Every Planar Graph with Some Sufficient Conditions but without 4- and 7-Cycles Is Weakly 2-Degenerate

作　　者：卢宏锴 

机构地区：[1]浙江师范大学,数学科学学院,浙江 金华

出　　处：《应用数学进展》2023年第10期4392-4402,共11页Advances in Applied Mathematics

摘　　要：如果一个图G的每个子图中有一个点v,它的度数最多为k,那么我们称图G为k-退化的。k-弱退化图是k-退化图的推广。在这篇文章中,我们证明了不含4圈,7圈和特殊圈的平面图是2-弱退化的, 同时也是3-DP-可染的。由此得到结论:每个不含4圈,k圈,7圈和9圈的平面图是2-弱退化的以及3-DP-可染的,这里k ∈ {5, 6}。A graph G is k-degenerate if its every subgraph contains a vertex of degree at mostk. Weakly k-degenerate graphs are a generalization of k-degenerate graphs. In this paper, we prove that every planar graph without 4, 7-cycles and some special cycles is weakly 2-degenerate. Consequently, it is 3-DP-colorable. As corollaries, every planar graph without 4-, k-, 7- and 9-cycles is weakly 2-degenerate and 3-DP-colorable, where k ∈ {5, 6}.

关 键 词：平面图 退化 弱退化 3-DP-可染 

分 类 号：O15[理学—数学]