Strong Chromatic Index in Subset Graphs

The strong chromatic index of a graph G, denoted sq(G), is the minimum number of parts needed to partition the edges of G into induced matchings. For 0 5 k 5 1 5 m, the subset graph S,(k, 1) is a bipartite graph whose vertices are the kand 1-subsets of an m element ground set where two vertices are adjacent if and only if one subset is contained in the other. We show that sq(Sm(k, 1 ) ) = (&) and that this number satisfies the strong chromatic index conjecture by Brualdi and Quinn for bipartite graphs. Further, we demonstrate that the conjecture is also valid for a more general family of bipartite graphs. @ 1997 John Wiley & Sons, Inc.