Seminar第2448讲 不同堆积序列的顶点临界图

创建时间:  2023年09月11日 19:45  谭福平   浏览次数:   

报告题目 (Title):Vertex-critical graphs for different packing sequences


报告人 (Speaker):史永堂 教授(南开大学)

报告时间 (Time):2023年9月21日 (周四) 10:00

报告地点 (Place):校本部F309,腾讯会议703655029


摘要:If $S=(s_1,s_2,\ldots)$ is a non-decreasing sequence of positive integers, then the $S$-packing $k$-coloring of a graph $G$ is a mapping $c: V(G)\rightarrow[k]$ such that if $c(u)=c(v)=i$ for $u\neq v\in V(G)$, then $d_G(u,v)>s_i$. The $S$-packing chromatic number of $G$ is the smallest integer $k$ such that $G$ admits an $S$-packing $k$-coloring. A graph $G$ is $\chi_S$-vertex-critical if $\chi_S(G-u) < \chi_S(G)$ for each $u\in V(G)$. If $G$ is $\chi_S$-vertex-critical and $\chi_S(G) = k$, then $G$ is $k$-$\chi_S$-vertex-critical. Results on $4$-$\chi_S$-vertex-critical graphs for sequences $S = (1,s_2, s_3, \ldots)$ with $s_2 \ge 3$ are characterized. Joint work with Shenwei Huang, Sandi Klav\v{z}ar, Hui Lei and Xiaopan Lian.

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