On intersections of interval graphs

Abstract

If one can associate with each vertex of a graph an interval of a line, so that two intervals intersect just when the corresponding vertices are joined by an edge, then one speaks of an interval graph. It is shown that any graph on v vertices is the intersection (“product”) of at most [ 1 2 v] interval graphs on the same vertex set. For v=2 k, k factors are necessary for, and only for, the complete k-partite graph K 2,2,…,2. Some results for the hypergraph generalization of this question are also obtained.