报告题目:Anti-Ramsey number of matchings in 3-uniform hypergraphs
报 告 人:鲁红亮,西安交通大学,教授
报告摘要: Let n, s, and k be positive integers such that k≥3, s≥3 and n≥ks. An s-matching Ms in a k-uniform hypergraph is a set of s pairwise disjoint edges. The anti-Ramsey number ar(n,k,Ms) of an s-matching is the smallest integer c such that each edge-coloring of the n-vertex k-uniform complete hypergraph with exactly c colors contains an s-matching with distinct colors. The value of ar(n,k,Ms) was conjectured by Ozkahya and Young(2013) for all n≥sk and k≥3. Frankl and Kupavskii(2019) verified this conjecture for all n≥ sk+(s-1)(k-1) and k≥3. We aim to determine the value of ar(n,3,Ms) for 3s ≤ n < 5s-2 in this paper. Namely, we prove that if 3s<n<5s-2 and n is large enough, then ar(n,3,Ms)=ex(n,3,Ms-1)+2. Here ex(n,3,Ms-1) is the Tura?n number of an (s-1)-matching. Thus this result confirms the conjecture of Ozkahya and Young for k=3, 3s<n<5s-2 and sufficiently large n. For n=ks and k≥3, we present a new construction for the lower bound of ar(n,k,Ms) which shows the conjecture by Ozkahya and Young is not true. In particular, for n=3s, we prove that ar(n,3,Ms)=ex(n,3,Ms-1)+5 for sufficiently large n.
报告人简介:鲁红亮,2010博士毕业于南开大学,现任西安交通大学数学院教授,博士生导师,曾受邀于第九届全国组合数学与图论大会做一小时大会报告,2020年荣获“陕西省青年科技奖”。主要研究图的度约束因子与超图的匹配问题,解决了多个图因子及匹配研究领域的公开问题及猜想;已发表及接受发表论文六十余篇,多篇论文发表在Sci. China Math.、SIAM DM、JGT、JCTA、JCTB、EJC等图论领域权威期刊上;共主持四项国家自然科学基金项目。
报告时间:2024年6月22日10:50-11:30
报告地点:文渊楼B208
主办单位:数学与统计学院