## On degree conditions for 2-factors with a prescribed number of cycles

Title：On degree conditions for 2-factors with a prescribed number of cycles

Speaker：日本熊本大学 Shuya Chiba 教授

Abstract：The hamiltonian problem has long been fundamental in graph theory. But, it is NP-complete, and so many researchers have focused on sufficient conditions for graphs to be hamiltonian. In particular, the following theorem, due to Ore (1960), is classical and well known in graph theory: If $G$ is a graph of order $n \ge 3$ and of $\sigma_{2}(G) \ge n$, then $G$ is hamiltonian, where $\sigma_{2}(G)$ denotes the minimum degree sum of two non-adjacent vertices in $G$. In this talk, as generalizations of this result, we introduce some degree conditions for the existence of a 2-factor with a prescribed number of cycles in graphs.

Shuya Chiba 教授简介：日本熊本大学教授，主要研究方向为极值组合和结构图论等方向，已在JCTB，SIAM Journal on Discrete Mathematics，Discrete Mathematics等图论顶级学术刊物发表学术论文30多篇。Shuya Chiba还获得了日本数学学会 2016 届 MSJ 优秀应用数学奖。