报 告 人：吕长虹 教授（华东师范大学）
报告题目：Path covering number and L(2; 1)-labeling number of graphs
报告时间：2016年9月17日下午4:30
报告地点：静远楼1506报告厅
报告摘要： A {\it path covering} of a graph $G$ is a set of vertex disjoint paths of $G$ containing all the vertices of $G$. The {\it path covering number} of $G$, denoted by $P(G)$, is the minimum number of paths in a path covering of $G$. An {\sl $k$-$L(2,1)$-labeling} of a graph $G$ is a mapping $f$ from $V(G)$ to the set $\{0,1,\ldots,k\}$ such that $|f(u)-f(v)|\ge 2$ if $d_G(u,v)=1$ and $|f(u)-f(v)|\ge 1$ if $d_G(u,v)=2$. The {\sl $L(2,1)$-labeling number $\lambda (G)$} of $G$ is the smallest number $k$ such that $G$ has a $k$-$L(2,1)$-labeling. The purpose of this paper is to study path covering number and $L(2,1)$-labeling number of graphs. Our main work extends most of results in [On island sequences of labelings with a condition at distance two, Discrete Applied maths 158 (2010), 1-7] and can answer an open problem in [On the structure of graphs with non-surjective $L(2,1)$-labelings, SIAM J. Discrete Math. 19 (2005), 208-223].
报告人简介：吕长虹，华东师范大学数学系副主任，教授，博士生导师。入选教育部新世纪优秀人才计划，上海市高校优秀青年教师，华东师范大学杰出新人奖。上海市工业与应用数学学会副理事长，中国工业与应用数学学会理事，中国运筹学会理事，上海数学学会理事。主持国家自然科学基金项目4项，主持企业委托项目3项，从事图论和组合优化方面的研究，发表sci 刊物论文30余篇。