Title: 3-colored asymmetric bipartite Ramsey number of connected matchings and cycles
Reporter: Prof. PENG Yuejian (Hunan University)
Time: November 3, 2018 (Saturday) AM 10:00-11:00
Location: A1101# room, Innovation Park Building
Contact: Prof. WANG Yi (tel:84708351-8128)
Abstract: Let k, l, m be integers and r(k, l, m) be the minimum integer N such that for any red-blue-green coloring of K(N,N), there is a red matching of size at least k in a component. or a blue matching of at least size l in a component, or a green matching of size at least m in a component. We determine the exact value of r(k, l, m) completely which answers a question of Bucic, Letzter, and Sudakov. Applying a technique originated by Luczak that applies Szemeredi's Regularity Lemma to reduce the problem of showing the existing in a component, we obtain the 3-colored asymmetric bipartite Ramsey number of cycles asymptotically. This is a joint work with Zhidan Luo.
The brief introduction to the reporter: Peng Yuejian is now a professor and doctoral supervisor at the school of mathematics and econometrics, Hunan University. He graduated from Emory University in 2001. In the 2001-2002 year, he worked as a Assistant Professor in the Mathematics Department of Chatham College in the US. From 2002 to 2012, he served in the Department of Mathematics and Computer Science at Indiana State University as an assistant professor, associate professor, and professor for life. His main research direction is combinatorial extremum problem, graph theory and its applications. Current research topics include the application of regular lemmas in graphs and hypergraphs, the extreme value problems in hypergraphs such as the Jumping Constant conjecture of Erds, the Turn edge density in hypergraphs and the Lagrangian and Ramsey-Turn problems in hypergraphs. He chaired two NSFC projects and published more than 40 papers in the authoritative international journals of combinatorial graph theory, such as Journal of Number Theory, Graphs and Combinatorics, Journal of Combinatorial Theory, Series A, Journal of Combinatorial Theory, Series B. He is currently a member of the Chinese Society of Industrial and Applied Mathematics, the Chinese Association of Mathematics Combinatorial Mathematics and Graph Theory Committee, and the Chinese Society of Industrial and Applied Mathematics, the Standing Committee of the Council of Graph Theory Combination.