: The decycling number (G) of a graph G is the smallest number of vertices which can be removed from G so that the resultant graph contains no cycles. In this paper, we study the d...
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...
The domatic number of a graph G is the maximum number of dominating sets into which the vertex set of G can be partitioned. We show that the domatic number of a random r-regular g...
Given any integer d ≥ 3, let k be the smallest integer such that d < 2k log k. We prove that with high probability the chromatic number of a random d-regular graph is k, k + 1...