报 告 人：赖虹建 教授（美国西弗吉尼亚大学）
报告题目：3-edge-connected supereulerian graphs and 3-conencted line graphs
报告时间：2015年12月3日上午9:00
报告地点：静远楼1508学术报告厅
摘要：For an integer $s_1, s_2, s_3 > 0$, let $N_{s_1, s_2, s_3}$ denote the graph obtained by identifying each vertex of a $K_3$ with an end vertex of three disjoint paths $P_{s_1+1}$, $P_{s_2+1}$, $P_{s_3+1}$ of length $s_1, s_2,$ and $s_3$, respectively. It has been a problem for determining the values of $s_1, s_2, s_3$ so that every 3-connected $\{K_{1,3}, N_{s_1,,s_2,s_3}\}$-free graph is Hamiltonian. Brousek, Ryj\'{a}\u{c}ek and Favaron (DM 1999) proved that every 3-connected $\{K_{1,3}, N_{4,0,0}\}$-free graph is Hamiltonian. There have been many people working on specific values of $s_1, s_2, s_3$ and quite a few research papers on the subject have been published. We in this talk will focus on our development of the “circumference control” method on the existence of supereulerian 3-edge-connected graphs, which allows us to characterize values of $s_1, s_2, s_3$ and exceptional graphs such that that every 3-connected $\{K_{1,3}, N_{s_1,,s_2,s_3}\}$-free graph is either Hamiltonian or has a structure as described by the exceptional graphs. (These are results in a paper [Discrete Math., 313 (2013), 784-795] and in a paper recently accepted by Discrete Applied Mathematics.)