# 11月18日　湖南大学彭岳建教授学术报告

Given two graphs $G$ and $H$, the Ramsey number $R(G,H)$ is the minimum integer $N$ such that  any coloring of the edges of $K_N$ in red or blue yields a red $G$ or a blue $H$. Let $\Delta(G)$ be the maximum degree of $G$, and $\chi(G)$ be the chromatic number of $G$.

Let $s(G)$ denote the chromatic surplus of $G$, the minimum cardinality of a color class taken over all proper colorings of $G$ with $\chi(G)$ colors. Burr  showed that for a connected graph $G$ and a graph $H$ with $v(G)\geq s(H)$, $R(G,H) \geq (v(G)-1)(\chi(H)-1)+s(H)$. A connected graph $G$ of order $n$ is called $H$-good if $R(G,H)=(n-1)(\chi(H)-1)+s(H)$. We will give some results related to Ramsey-goodness in this talk.