Speaker: Shi Yongtang, Professor, doctoral supervisor at Nankai University

Date: November 4, 2022

Time: 14:00-15:00

Location: Zoom

Sponsor: School of Mathematics, Shandong University

Abstract:

For an integer l≥2 , the l-connectivity κ_l (G) of a graph G is defined to be the minimum number of vertices of G whose removal produces a disconnected graph with at least l components or a graph with fewer than l vertices. The l-edge-connectivity λ_l (G) of a graph G is the minimum number of edges whose removal leaves a graph with at least l components if |V(G)|≥l, and λ_l (G)=|E(G)| if |V(G)|<l. Given integersk≥0andl≥2,we investigate κ_l (G(n,p)) and λ_l (G(n,p)) when np≤log⁡n+kloglogn . Furthermore, our arguments can be used to show that in the random graph process, the hitting times of minimum degree at least k and of l-connectivity (or l-edge-connectivity) at least k(l-1) coincide with high probability. These results generalize the work of Bolloba ́s and Thomason on classical connectivity.

For more information, please visit:

https://www.view.sdu.edu.cn/info/1020/171510.htm