Upper bounds to the clique width of graphs
Discrete Applied Mathematics
Approximating clique-width and branch-width
Journal of Combinatorial Theory Series B
Rank-width is less than or equal to branch-width
Journal of Graph Theory
On the threshold of having a linear treewidth in random graphs
COCOON'06 Proceedings of the 12th annual international conference on Computing and Combinatorics
European Journal of Combinatorics
A SAT approach to clique-width
SAT'13 Proceedings of the 16th international conference on Theory and Applications of Satisfiability Testing
On the tree-depth of random graphs
Discrete Applied Mathematics
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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∈(0, 1) is a constant, then rw(G(n, p)) = ⌈n/3⌉−O(1), (ii) if , then rw(G(n, p)) = ⌈1/3⌉−o(n), (iii) if p = c/n and c1, 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 c1, answering a question of Gao [2006]. © 2011 Wiley Periodicals, Inc. J Graph Theory, © 2012 Wiley Periodicals, Inc. (Contract grant sponsors: Samsung Scholarship (to C. L.); National Research Foundation of Korea (NRF); Contract grant number: 2011-0001185 (to J. L. and S. O.); Contract grant sponsor: TJ Park Junior Faculty Fellowship (to S. O.).)