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https://open.uns.ac.rs/handle/123456789/14182
Title: | A sharp threshold for the hamilton cycle Maker-Breaker game | Authors: | Hefetz D. Krivelevich M. Stojaković, Miloš Szabó T. |
Issue Date: | 1-Jan-2009 | Journal: | Random Structures and Algorithms | Abstract: | We study the Hamilton cycle Maker-Breaker game, played on the edges of the random graph G(n,p). We prove a conjecture from (Stojaković and Szabó, Random Struct and Algorithms 26 (2005), 204-223.), asserting that the property that Maker is able to win this game, has a sharp threshold at log n/n. Our theorem can be considered a game-theoretic strengthening of classical results from the theory of random graphs: not only does G(n,p) almost surely admit a Hamilton cycle for p = (1 + ε) log n/n, but Maker is able to build one while playing against an adversary. © 2008 Wiley Periodicals, Inc. | URI: | https://open.uns.ac.rs/handle/123456789/14182 | ISSN: | 10429832 | DOI: | 10.1002/rsa.20252 |
Appears in Collections: | PMF Publikacije/Publications |
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