Let G be a d-regular graph with girth g, and let α be the independence number of G. We show that α(G) ≥ 1 2 1 − (d − 1)−2/(d−2) − (g) n where (g) → 0 as g → ∞,...
Abstract. We present algorithmic lower bounds on the size of the largest independent sets of vertices in a random d-regular graph. Our bounds hold with probability approaching one ...