The strong chromatic index of random graphs

Alan Frieze*, Michael Krivelevich, Benny Sudakov

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

The strong chromatic index of a graph G, denoted by χ s(G), is the minimum number of colors needed to color its edges so that each color class is an induced matching. In this paper we analyze the asymptotic behavior of this parameter in a random graph G(n, p), for two regions of the edge probability p = p(n). For the dense case, where p is a constant, 0 < p < 1, we prove that with high probability χ s(G) ≤ (1 + o(1))3/4 n 2p/log b n, where 6 = 1/(1 - p). This improves upon a result of Czygrinow and Nagle [Discrete Math., 281 (2004), pp. 129-136]. For the sparse case, where np < 1/100 √log n/log log n, we show that with high probability χ s(G) = Δ 1(G), where Δ 1(G) = max{d(u) + d(v) - 1 : (u, v) ∈ E(G)}. This improves a result of Palka [Australas. J. Combin., 18 (1998), pp. 219-226].

Original languageEnglish
Pages (from-to)719-727
Number of pages9
JournalSIAM Journal on Discrete Mathematics
Volume19
Issue number3
DOIs
StatePublished - 2005

Keywords

  • Random graphs
  • Strong chromatic index

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