Optimal edge coloring of large graphs

Most of the general families of large considered graphs in the context of t he so-called (Delta, D) problem - that is, how to obtain graphs with maximu m order, given their maximum degree Delta and their diameter D-known up to now for any value of Delta and D, are obtained as product graphs, compound graphs, and generalized compound graphs. It is shown that many of these gra ph constructions have a minimum chromatic index Delta. Optimal edge colorin g of large (Delta, D) graphs is interesting, for instance, for the design o f large packet radio networks. Furthermore, a complete table with the best- known edge-colored large graphs is also presented for 2 less than or equal to D less than or equal to 10. (C) 1999 John Wiley & Sons, Inc. Networks 34 : 61-65, 1999.