报告题目On heavy subgraph conditions for Hamiltonicity of graphs

报告人：宁博，天津大学应用数学中心

报告时间：11月13日 16:30-17:30

地点：1208

摘要：

Hamiltonian problem may be one of the most important problems in structural graph theory. There are two kinds of sufficient conditions for Hamiltonicity of graphs. One is the so-called degree condition, and among them, Ore' condition and Fan's condition are famous. The other is the structural condition, and forbidden subgraph condition plays a central role. Generally speaking, heavy subgraph condition is a combination of degree condition and forbidden subgraph condition. In this talk, we will give a short survey on several works on Hamiltonicity under Ore-type and Fan-type heavy subgraph conditions. We will also include an affirmation of a conjecture of Broersma, which was proposed on the workshop C&C (Novy Smokovec, 1993), up to an additive constant. In particular, we will give our recent work on Hamilonicity of graphs under so-called clique-heavy condition. This recent work is closely related to a previous theorem of Professor Z.-Q Hu. (Z.-Q, Hu, A generalization of Fan's condition and forbidden subgraph conditions for Hamiltonicity, Discrete Math. 196 (1999), no. 1�3, 167�175.)