Rank-width of random graphs

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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), 514528]. 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 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 tree-width of G(n, p) is linear in n whenever p = c/n for each c>1, answering a question of Gao [2006]. (c) 2011 Wiley Periodicals, Inc. J Graph Theory.
Publisher
WILEY-BLACKWELL
Issue Date
2012-07
Language
English
Article Type
Article
Citation

JOURNAL OF GRAPH THEORY, v.70, no.3, pp.339 - 347

ISSN
0364-9024
DOI
10.1002/jgt.20620
URI
http://hdl.handle.net/10203/103163
Appears in Collection
MA-Journal Papers(저널논문)
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