%L discovery10120245 %I Wiley %O This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. %J Journal of Graph Theory %A C Lee %A J Lee %A S-I Oum %X Rankâ€width of a graph G, denoted by rw(G), is a width parameter of graphs introduced by Oum and Seymour [J Combin Theory Ser B 96 (2006), 514–528]. We investigate the asymptotic behavior of rankâ€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)) = ⌈n/3⌉−O(1), (ii) if urn:x-wiley:03649024:jgt20620:equation:jgt20620-math-0001, then rw(G(n, p)) = ⌈1/3⌉−o(n), (iii) if p = c/n and c>1, then rw(G(n, p))⩾rn for some r = r(c), and (iv) if p⩽c/n and c81, then rw(G(n, p))⩽2. As a corollary, we deduce that the treeâ€width of G(n, p) is linear in n whenever p = c/n for each c>1, answering a question of Gao [2006]. %P 339-347 %N 3 %T Rank-width of random graphs %D 2012 %V 70