Speaker: Tuan Tran, professor, University of Science and Technology of China

Date: May 24, 2024

Time: 14:30-16:30

Location: E119, Huagangyuan Building, Qingdao Campus

Sponsor: Frontiers Science Center for Nonlinear Expectations, Shandong University; Research Centre for Mathematics and Interdisciplinary Sciences Centre, Shandong University; Sino-Russian Mathematics Center in Qingdao

Abstract:

Consider a multipartite graph G with maximum degree at most n−o(n), parts V1,…,Vk have size |Vi|=n, and every vertex has at most o(n) neighbors in any part Vi. Loh and Sudakov proved that any such G has an independent transversal. They further conjectured that the vertex set of G can be decomposed into pairwise disjoint independent transversals. In the present paper, we resolve this conjecture approximately by showing that G contains n−o(n) pairwise disjoint independent transversals. As applications, we give approximate answers to questions of Yuster, and of Fischer, Kühn, and Osthus. Joint work with Debsoumya Chakraborti.

For more information, please visit:

https://www.view.sdu.edu.cn/info/1020/191583.htm