Regular subgraphs of random graphs

In this paper, we prove that there exists a function k = (4 + o(1))k such that G(n, /n) contains a k-regular graph with high probability whenever > k. In the case of k = 3, it is also shown that G(n, /n) contains a 3-regular graph with high probability whenever > 5.1494. These are the first constant bounds on the average degree in G(n, p) for the existence of a k-regular subgraph. We also discuss the appearance of 3-regular subgraphs in cores of random graphs.

• Type: Journal
• Year: 2006
• Where: RSA
• Authors: Béla Bollobás, Jeong Han Kim, Jacques Verstraëte
• Keywords: 3-regular Graph, K-regular Graph, Paper, RSA 2006