报告题目：不含$K_5$作为子式的图的边染色、全染色和线性荫度

主 讲 人：吴 建 良

单 位：山东大学

时 间：8月11日14:30

腾 讯 ID：997 599 328

密 码：123456

摘 要：

To identify nonadjacent vertices $x$ and $y$ of a graph $G$ is to replace these vertices by a single vertex incident with all the edges which were incident in $G$ with either $x$ or $y$. Let $e=xy \in E(G)$. To contract an edge $e$ of a graph $G$ is to delete the edge and then identify its ends. A graph $H$ is a minor of a graph $G$ if $G$ has a subgraph contractible to $H$; $G$ is called $H$-minor free if $G$ does not have $H$ as a minor. Recently, we obtain the following results.

Theorem：Let $G$ be a $K_{5}$-minor free graph.

(I) If $\Delta(G)\geq 7$,then $\chi'(G) =\Delta(G)$;

(II) $\lceil\frac{\Delta(G)}{2}\rceil\leq la(G) \leq\lceil\frac{\Delta(G)+1}{2}\rceil$. Moreover, if $\Delta(G)\geq 9$, then $la(G)= \lceil\frac{\Delta(G)}{2}\rceil$;

(III) If $\Delta(G)\geq 7$,then $\chi''(G) =\Delta(G)+2$. Moreover, if $\Delta(G)\geq 10$, then $\chi''(G)=\Delta(G)+1$.

简 介：

吴建良，山东大学教授、博士生导师。现为中国系统工程学会理事、中国工业与应用数学学会组合图论及应用专业委员会副主任委员、中国运筹学会图论组合分会常务委员、中国数学会组合数学与图论专业委员会委员。到目前为止正式发表学术的论文有180余篇，主持和参与各类基金15余项，目前主持国家自然科学基面上项目和山东省自然科学基金各1项，参与国家自然科学基金重点项目1项。