@article{discovery10120245,
       publisher = {Wiley},
            note = {This version is the author accepted manuscript. For information on re-use, please refer to the publisher's terms and conditions.},
           pages = {339--347},
         journal = {Journal of Graph Theory},
           month = {July},
           title = {Rank-width of random graphs},
          number = {3},
          volume = {70},
            year = {2012},
             url = {https://doi.org/10.1002/jgt.20620},
          author = {Lee, C and Lee, J and Oum, S-I},
        abstract = {Rank-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 rank-width of a random graph G(n, p). We show that, asymptotically almost surely, (i) if p{$\in$}(0, 1) is a constant, then rw(G(n, p)) = {$\lceil$}n/3{$\rceil$}?O(1), (ii) if urn:x-wiley:03649024:jgt20620:equation:jgt20620-math-0001, then rw(G(n, p)) = {$\lceil$}1/3{$\rceil$}?o(n), (iii) if p = c/n and c{\ensuremath{>}}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 tree-width of G(n, p) is linear in n whenever p = c/n for each c{\ensuremath{>}}1, answering a question of Gao [2006].},
            issn = {0364-9024}
}