Rank-width of random graphs

Abstract

Rank-width of a graph G, denoted by rw(G), is a width parameter of graphs introduced by Oum and Seymour (2006). We investigate the asymptotic behavior of rank-width of a random graph G(n, p). We show that, asymptotically almost surely, (i) if p ∈ (0, 1) is a constant, then rw(G(n, p)) = dn3 e −O(1), (ii) if 1 n p ≤ 1 2 , then rw(G(n, p)) = d n 3 e − o(n… (More)
DOI: 10.1002/jgt.20620

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