主 讲 人 ：宋梓霞    教授

活动时间：2025-07-08 08:30:00

地      点 ：Zoom会议 https://us06web.zoom.us/j/85222901621?pwd=tc0A4yhtMxyulAsxLI3OZHdl340yPu.1 会议号: 852 2290 1621 密码: 592639

主办单位：数学科学学院

讲座内容：

For positive integers n,m, the double star S(n,m) is the graph consisting of the disjoint union of two stars K_{1,n} and K_{1,m} together with an edge joining their centers. Finding monochromatic copies of double stars in edge-colored complete graph and complete bipartite graphs has attracted much attention. The k-color Ramsey number and bipartite Ramsey number of S(n,m) are denoted by r(S(n,m);k) and r_{bip}(S(n,m);k), respectively. To the best of our knowledge, little is known on the exact value of r(S(n,m);k) and r_{bip}(S(n,m);k) when k\ge 3. Using a folklore double counting argument in set system and the edge chromatic number of complete graphs, we prove that if k is odd and n is sufficiently large compared with m and k, then \[r(S(n,m);k)=kn+m+2.\] Applying the Turán argument in the bipartite setting, we prove that if k=2 and n\ge m, or k\ge 3 and n\ge 2m, then \[br(S(n,m);k) = kn + 1.\] In this talk we will discuss the main ideas of our results.

This is joint work with Jake Ruotolo (Harvard University) and Gregory DeCamillis (University of Waterloo).

主讲人介绍：

宋梓霞，美国中佛罗里达大学（University of Central Florida）数学系系主任、教授、博士生导师，主要研究方向为图论。1990–1994年于安徽大学获学士学位，1994–1997年于中国科学技术大学获硕士学位，2000–2004年于美国佐治亚理工学院获算法、组合与优化博士学位，2004–2005年在俄亥俄州立大学从事博士后研究。2005年起任教于中佛罗里达大学，主持美国国家安全局（NSA）和国家科学基金会（NSF）科研项目，并担任NSF评审专家。曾获校优秀教学奖与科研奖。其研究成果发表于 Advances in Mathematics、Journal of Combinatorial Theory, Series B、Combinatorica、SIAM Journal on Discrete Mathematics、Journal of Graph Theory 等图论领域国际权威期刊，现任 Discrete Mathematics 编委（Associate Editor）。