# 12月21日 宋梓霞教授学术报告（数学与统计学会）

A  hole  in a graph  is an induced cycle of length at least $4$.  Let $s\ge2$ and $t\ge2$ be integers.  A graph $G$ is \dfn{$(s,t)$-splittable} if$V(G)$ can be partitioned into two sets $S$ and $T$ such that $\chi(G[S ]) \ges$ and $\chi(G[T ]) \ge t$.

The well-knownErd\H{o}s-Lov\'asz Tihany Conjecture from 1968 states that every  graph $G$ with $\omega(G) < \chi(G) = s +t - 1$ is $(s,t)$-splittable.

This conjecture is hard,and  few related results are known.  However, it has been verified to be true forline graphs, quasi-line graphs, and graphs with independence number $2$. Inthis talk, we will present some recent progress on  Erd\H{o}s-Lov\'asz Tihany Conjecture.

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