学术报告报告题目：Tree-Star Ramsey Numbers
报 告 人：彭岳建 教授 (湖南大学)
报告时间：2020年12月26日（星期六）上午 10:30-11:30
报告地点：腾讯会议，会议ID号：957 629 038，密码：123456
邀 请 人：林鸿莺 博士
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数学学院
2020年12月24日
报告摘要：
Let Tn be a tree on n vertices and K1, m be the star with m+1 vertices. For graphs G and H, the Ramsey Number R(G, H) is the smallest integer N such that any red-blue-coloring of the edges of KN yields a red G or a blue H. A well-known result is that if G is a graph with minimum degree n-1, then Tn can be embedded into G. Applying this result, Burr gave an upper bound for the Ramsey number R(Tn, K1, m) and determined the exact value of R(Tn, K1, m) for some cases. Guo and Volkmann showed that if G is a connected graph with at least n vertices and minimum degree n-2, then Tn can be embedded into G except Tn=K1, n-1. Applying this, they improved that bound of R(Tn, K1, m) in the result of Burr by 1 for some cases and obtain the exact value of R(Tn, K1, m) for some cases in addition to Burr's result. Guo and Volkmann also conjectured that if G is a connected graph with at least n vertices and minimum degree n-3, then Tn with maximum degree ≤n-4 can be embedded into G. In this paper, we obtain a sufficient and necessary condition that Tn with maximum degree ≤n-3 can be embedded into a connected graph G with at least n vertices and minimum degree ≥n-3. Our result implies that the conjecture of Guo and Volkmann is true with one exception. Applying this result, we improve the upper bound of R(Tn, K1, m) and determine the exact value of R(Tn, K1, m) for some cases. (This is a joint work with Yan Zi-Long.)
报告人简介：
彭岳建，湖南大学教授，博士生导师。主要从事极值组合与图论及相关领域的研究。2001年于美国埃默里大学（Emory University）获得理学博士学位。2002-2012年在美国印第安纳州立大学（Indiana State University）历任助理教授、副教授、教授（终身）。2012年作为“湖南省百人计划”特聘教授回到湖南大学。目前，在国际组合图论权威刊物JCTB、JCTA、CPC、JNT（数论杂志）等发表论文五十多篇。主持国家自然科学基金重点项目。