Abstract: | We give constructions of bipartite graphs with maximum Δ, diameter D on B vertices, such that for every D ≥ 2 the lim infΔ→∞B. Δ1-D = bD > 0. We also improve similar results on ordinary graphs, for example, we prove that limΔ→∞N · Δ?D = 1 if D is 3 or 5. This is a partial answer to a problem of Bollobás. |