Minimal Universal Bipartite Graphs

A graph U is (induced)-universal for a class of graphs X if every member of X is contained in U as an induced subgraph. We study the problem of finding a universal graph with minimum number of vertices for various classes of bipartite graphs: exponential classes of bipartite (and general) graphs, bipartite chain graphs, bipartite permutation graphs, and general bipartite graphs. For exponential classes and general bipartite graphs we present a construction which is asymptotically optimal while for the other classes our solutions are optimal in order.