The small subgraph conditioning method first appeared when Robinson and the second author showed the almost sure hamiltonicity of random d-regular graphs. Since then it has been u...
An old problem of Erd˝os, Fajtlowicz and Staton asks for the order of a largest induced regular subgraph that can be found in every graph on n vertices. Motivated by this problem...
Michael Krivelevich, Benny Sudakov, Nicholas C. Wo...
Let G be a regular graph and H a subgraph on the same vertex set. We give surprisingly compact formulas for the number of copies of H one expects to find in a random subgraph of G...
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...