For a graph 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,χs(G), is the smallest number of colors in a strong edge coloring of G. Palka (Austral. J. Combin. 18 (1998) 219-226), proved that if p=p(n)=Θ(n-1), then with high probability, χ s(G(n,p))=O(Δ(G(n,p))). Recently Vu (Combin. Probab. Comput. 11 (2002) 103-111), proved that if n-1(lnn) 1+δ≤p=p(n)≤n-ε for any 0<ε,δ<1, then with high probability, χ s(G(n,p))=O((pn)2/ln(pn)). In this note, we prove that if p=p(n)>n-ε for all ε>0, then with b=(1-p) -1, with high probability, (1-o(1))(pn2/log bn)≤χs(G(n,p))≤(2+o(1))(pn2/logbn).
- Random graphs
- Strong chromatic index
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics