A sharp threshold for the hamilton cycle Maker-Breaker game

Dan Hefetz; Michael Krivelevich; Miloš Stojakovič; Tibor Szabó

doi:10.1002/rsa.20252

A sharp threshold for the hamilton cycle Maker-Breaker game

Dan Hefetz^*, Michael Krivelevich, Miloš Stojakovič, Tibor Szabó

^*Corresponding author for this work

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	112-122
Number of pages	11
Journal	Random Structures and Algorithms
Volume	34
Issue number	1
DOIs	https://doi.org/10.1002/rsa.20252
State	Published - Jan 2009

Keywords

Combinatorial games
Hamilton cycle
Random graph

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10.1002/rsa.20252

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title = "A sharp threshold for the hamilton cycle Maker-Breaker game",

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 (Stojakovi{\'c} and Szab{\'o}, 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.",

keywords = "Combinatorial games, Hamilton cycle, Random graph",

author = "Dan Hefetz and Michael Krivelevich and Milo{\v s} Stojakovi{\v c} and Tibor Szab{\'o}",

year = "2009",

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doi = "10.1002/rsa.20252",

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AU - Krivelevich, Michael

AU - Stojakovič, Miloš

AU - Szabó, Tibor

PY - 2009/1

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N2 - 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.

AB - 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.

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JO - Random Structures and Algorithms

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ER -

A sharp threshold for the hamilton cycle Maker-Breaker game

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Keywords

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