Embedding arbitrary finite simple graphs into small strongly regular graphs

It is well-known that any nite simple graph ? is an induced sub-graph of some exponentially larger strongly regular graph ? (e.g. 2, 8]). No general polynomial-size construction has been known. For a given-nite simple graph ? on v vertices we present a construction of a strongly regular graph ? on O(v 4) vertices that contains ? as its induced sub-graph. A discussion is included of the size of the smallest possible strongly regular graph with this property.