TY - JOUR

T1 - The strong chromatic index of random graphs

AU - Frieze, Alan

AU - Krivelevich, Michael

AU - Sudakov, Benny

PY - 2005

Y1 - 2005

N2 - 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].

AB - 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].

KW - Random graphs

KW - Strong chromatic index

UR - http://www.scopus.com/inward/record.url?scp=33747188408&partnerID=8YFLogxK

U2 - 10.1137/S0895480104445757

DO - 10.1137/S0895480104445757

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AN - SCOPUS:33747188408

SN - 0895-4801

VL - 19

SP - 719

EP - 727

JO - SIAM Journal on Discrete Mathematics

JF - SIAM Journal on Discrete Mathematics

IS - 3

ER -