부산대학교 도서관

Summary: ``Let $G$ be a graph, and let ${\rm cl}(G)$ denote the clique number of $G$. The notation $G\to(3,3)$ means that in any 2-partition $V_1\cup V_2$ of the set $V(G)$ of vertices either $V_1$ or $V_2$ contains a 3-clique (triangle) of $G$; $\alpha=\min\{|V(G)|\colon\ G\to(3,3)$ and ${\rm cl}(G)=4\}$, $\beta=\min\{|V(G)|\colon\ G\to(3,3)$ and ${\rm cl}(G)=3\}$. In this article, we consider graphs $G$ with the property $G\to(3,3)$. As a consequence it follows from proven results that $\alpha=8$ and $\beta\geq 12$.''