美国西弗吉尼亚大学Prof. Lai Hong-Jian学术报告(运筹学讨论班)

题 目: Some Recent Progresses on Hamiltonian Line Graphs
报告人：Prof. Lai Hong-Jian（美国西弗吉尼亚大学）
时 间：5月14日 10：30-11：30
地 点：理科大楼A 1510
Abstract: We shall present a summary of recent results we have done in this area, and methods we have developed in working on these problems. In particular, we have proved the following results.
(i) (Conjectured by Ryjacek in 1990) Every 3-connected, locally $N_2$-connected claw-free graph is hamiltonian. large
(ii) (Conjectured by Kuipers and Veldman in 1996) If $H$ is a 3-connected claw-free graph with sufficiently order $n$, and if $delta(H)ge frac{n+5}{10}$, then either $H$ is hamiltonian, or $delta(H)=frac{n+5}{10}$ and $H$ can be constructed from the Petersen graph.
(iii) Every 3-connected, essentially 11-connected line graph is hamiltonian.
(iv) For $s ge 5$, a line graph $L(G)$ is $s$-hamiltonian connected if and only if $L(G)$ is $(s+2)$-connected.
(v) Every 3-connected, ${K_{1,3}, Z_9}$-free graph is hamiltonian.