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 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...
We study ways to expedite Yates's algorithm for computing the zeta and Moebius transforms of a function defined on the subset lattice. We develop a trimmed variant of Moebius ...
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...