Large bipartite graphs with given degree and diameter

Abstract

Abstract We give constructions of bipartite graphs with maximum Δ, diameter D on B vertices, such that for every D ≥ 2 the lim inf Δ→∞ B . Δ 1‐D = b D > 0. We also improve similar results on ordinary graphs, for example, we prove that lim Δ→∞ N · Δ −D = 1 if D is 3 or 5. This is a partial answer to a problem of Bollobás.