报告题目 (Title)：Vertex-critical graphs for different packing sequences
中文题目：不同堆积序列的顶点临界图
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
邀请人(Inviter)：何卓衡
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.