ASYMPTOTIC ENUMERATION OF FULL GRAPHS

A full graph on n vertices, as defined by Fulkerson, is a representation of the intersection and containment relations among a system of n sets. It has an undirected edge between vertices representing intersecting sets, and a directed edge from a to b if the corresponding set A contains B. We give a unified argument to show that asymptotically, almost all full graphs can be obtained by taking an arbitrary undirected graph in the n vertices, distinguishing a clique in this graph that need not be maximal, and then adding directed edges going out from each vertex in the clique to all vertices to which there is not already an existing undirected edge. (C) 1995 John Wiley and Sons, Inc.