Topic: K4-Factor in Random Graphs
Speaker: Professor Cai Jiansheng
Event date: 10/12/2019
Event time: 14:00 pm
Venue: Lecture Hall 204, Building 9
Sponsor: School of Mathematics and Statistics, Institute of Science and Technology
Abstract:
For a graph $G$ with $n$vertices, where $4$ divides $n$, a $K_4$-factor is a subgraph of $G$.consisting of $n/4$ vertex disjoint $K_4$. We consider the minimal probability$p=p(n)$, for which a random graph $G=G(n,p)$ almost surely contains a$K_{4}$-factor. In this paper, we prove that for $p=O(n^{-0.49})$, the random graph $G(n,p)$ almost surely contains a $K_4$-factor.