Optimal edge coloring of large graphs

Abstract

Most of the general families of large considered graphs in the context of the so-called (A, D) problem-that is, how to obtain graphs with maximum order, given their maximum degree Δ and their diameter D-known up to now for any value of Δ and D, are obtained as product graphs, compound graphs, and generalized compound graphs. It is shown that many of these graph constructions have a minimum chromatic index A. Optimal edge coloring of large (A, D) graphs is interesting, for instance, for the design of large packet radio networks. Furthermore, a complete table with the best-known edge-colored large graphs is also presented for 2 ≤ D ≤ 10.