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**1 - 2**of**2**### Strong Edge Colorings of Uniform Graphs

, 2003

"... For a graph G = (V (G); E(G)), a strong edge coloring of G is an edge coloring in which every color class is an induced matching. The strong chromatic index of G, s(G), is the smallest number of colors in a strong edge coloring of G. The strong chromatic index of the random graph G(n; p) was conside ..."

Abstract
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For a graph G = (V (G); E(G)), a strong edge coloring of G is an edge coloring in which every color class is an induced matching. The strong chromatic index of G, s(G), is the smallest number of colors in a strong edge coloring of G. The strong chromatic index of the random graph G(n; p) was considered in [2], [3], [11], and [14]. In this paper, we consider s(G) for a related class of graphs G known as uniform or -regular graphs. In particular, we prove that for 0 < d < 1, all (d; )-regular bipartite graphs G = (U [ V;E) with jU j = jV j n0(d; ) satisfy s(G) ()(G) 2, where () ! 0 as ! 0 (this order of magnitude is easily seen to be best possible). Our main tool in proving this statement is a powerful packing result of Pippenger and Spencer [10].