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Tuesday, January 27, 2004

**Abstract:** A strong edge-coloring of a graph *G* is an edge-coloring in which every color class is an induced matching; that is, if *uv* and *wz* have the same color, then the subgraph induced by those four vertices has only those two edges. The strong chromatic index *s'(G)* is the minimum integer number of colors in a strong edge-coloring of *G*. Brualdi and Quinn conjectured that for every bipartite graph *G*, *s'(G)* is bounded by *D _{1} D_{2}*, where

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