Ramsey games with giants

Tom Bohman; Alan Frieze; Michael Krivelevich; Po Shen Loh; Benny Sudakov

doi:https://doi.org/10.1002/rsa.20343

Ramsey games with giants

Tom Bohman, Alan Frieze, Michael Krivelevich, Po Shen Loh, Benny Sudakov

School of Mathematical Sciences

Tel Aviv University

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

Abstract

The classical result in the theory of random graphs, proved by Erdos and Rényi in 1960, concerns the threshold for the appearance of the giant component in the random graph process. We consider a variant of this problem, with a Ramsey flavor. Now, each random edge that arrives in a sequence of rounds must be colored with one of r colors. The goal can be either to create a giant component in every color class, or alternatively, to avoid it in every color. One can analyze the offline or online setting for this problem. In this paper, we consider all these variants and provide nontrivial upper and lower bounds; in certain cases (like online avoidance) the obtained bounds are asymptotically tight.

Original language	English
Pages (from-to)	1-32
Number of pages	32
Journal	Random Structures and Algorithms
Volume	38
Issue number	1-2
DOIs	https://doi.org/10.1002/rsa.20343
State	Published - Jan 2011

Keywords

Giant component
Ramsey game
Random graphs

All Science Journal Classification (ASJC) codes

Software
Applied Mathematics
General Mathematics
Computer Graphics and Computer-Aided Design

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https://doi.org/10.1002/rsa.20343

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title = "Ramsey games with giants",

abstract = "The classical result in the theory of random graphs, proved by Erdos and R{\'e}nyi in 1960, concerns the threshold for the appearance of the giant component in the random graph process. We consider a variant of this problem, with a Ramsey flavor. Now, each random edge that arrives in a sequence of rounds must be colored with one of r colors. The goal can be either to create a giant component in every color class, or alternatively, to avoid it in every color. One can analyze the offline or online setting for this problem. In this paper, we consider all these variants and provide nontrivial upper and lower bounds; in certain cases (like online avoidance) the obtained bounds are asymptotically tight.",

keywords = "Giant component, Ramsey game, Random graphs",

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AB - The classical result in the theory of random graphs, proved by Erdos and Rényi in 1960, concerns the threshold for the appearance of the giant component in the random graph process. We consider a variant of this problem, with a Ramsey flavor. Now, each random edge that arrives in a sequence of rounds must be colored with one of r colors. The goal can be either to create a giant component in every color class, or alternatively, to avoid it in every color. One can analyze the offline or online setting for this problem. In this paper, we consider all these variants and provide nontrivial upper and lower bounds; in certain cases (like online avoidance) the obtained bounds are asymptotically tight.

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JO - Random Structures and Algorithms

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Ramsey games with giants

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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