Picker-Chooser fixed graph games

Małgorzata Bednarska-Bzdȩga; Dan Hefetz; Tomasz Łuczak

doi:10.1016/j.jctb.2015.12.008

Picker-Chooser fixed graph games

Małgorzata Bednarska-Bzdȩga, Dan Hefetz, Tomasz Łuczak

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

8 Scopus citations

Abstract

Given a fixed graph H and a positive integer n, a Picker-Chooser H-game is a biased game played on the edge set of K_n in which Picker is trying to force many copies of H and Chooser is trying to prevent him from doing so. In this paper we conjecture that the value of the game is roughly the same as the expected number of copies of H in the random graph G(n, p) and prove our conjecture for special classes of graphs H such as complete graphs and trees.

Original language	English
Pages (from-to)	122-154
Number of pages	33
Journal	Journal of Combinatorial Theory. Series B
Volume	119
DOIs	https://doi.org/10.1016/j.jctb.2015.12.008
State	Published - 1 Jul 2016
Externally published	Yes

Keywords

Counting subgraphs
Positional games
Probabilistic intuition
Random graphs
Talagrand's inequality
Threshold function

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10.1016/j.jctb.2015.12.008

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title = "Picker-Chooser fixed graph games",

abstract = "Given a fixed graph H and a positive integer n, a Picker-Chooser H-game is a biased game played on the edge set of Kn in which Picker is trying to force many copies of H and Chooser is trying to prevent him from doing so. In this paper we conjecture that the value of the game is roughly the same as the expected number of copies of H in the random graph G(n, p) and prove our conjecture for special classes of graphs H such as complete graphs and trees.",

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AU - Łuczak, Tomasz

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N2 - Given a fixed graph H and a positive integer n, a Picker-Chooser H-game is a biased game played on the edge set of Kn in which Picker is trying to force many copies of H and Chooser is trying to prevent him from doing so. In this paper we conjecture that the value of the game is roughly the same as the expected number of copies of H in the random graph G(n, p) and prove our conjecture for special classes of graphs H such as complete graphs and trees.

AB - Given a fixed graph H and a positive integer n, a Picker-Chooser H-game is a biased game played on the edge set of Kn in which Picker is trying to force many copies of H and Chooser is trying to prevent him from doing so. In this paper we conjecture that the value of the game is roughly the same as the expected number of copies of H in the random graph G(n, p) and prove our conjecture for special classes of graphs H such as complete graphs and trees.

KW - Counting subgraphs

KW - Positional games

KW - Probabilistic intuition

KW - Random graphs

KW - Talagrand's inequality

KW - Threshold function

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JO - Journal of Combinatorial Theory. Series B

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ER -

Picker-Chooser fixed graph games

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Keywords

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