Creating small subgraphs in achlioptas processes with growing parameter

Michael Krivelevich; Reto Spöhel

doi:https://doi.org/10.1137/110836146

Creating small subgraphs in achlioptas processes with growing parameter

Michael Krivelevich, Reto Spöhel

School of Mathematical Sciences

Tel Aviv University

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

Abstract

We study the problem of creating a copy of some fixed graph H in the Achlioptas process on n vertices with parameter r, where r = r(n) is a growing function of n. We prove general upper and lower bounds on the threshold of this problem, and derive exact threshold functions for the case where H is a tree, a cycle, or the complete graph on four vertices.

Original language	English
Pages (from-to)	670-686
Number of pages	17
Journal	SIAM Journal on Discrete Mathematics
Volume	26
Issue number	2
DOIs	https://doi.org/10.1137/110836146
State	Published - 2012

Keywords

Achlioptas process
Power of choices
Random graph
Small subgraph
Threshold

All Science Journal Classification (ASJC) codes

General Mathematics

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https://doi.org/10.1137/110836146

Cite this

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abstract = "We study the problem of creating a copy of some fixed graph H in the Achlioptas process on n vertices with parameter r, where r = r(n) is a growing function of n. We prove general upper and lower bounds on the threshold of this problem, and derive exact threshold functions for the case where H is a tree, a cycle, or the complete graph on four vertices.",

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AB - We study the problem of creating a copy of some fixed graph H in the Achlioptas process on n vertices with parameter r, where r = r(n) is a growing function of n. We prove general upper and lower bounds on the threshold of this problem, and derive exact threshold functions for the case where H is a tree, a cycle, or the complete graph on four vertices.

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KW - Threshold

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Creating small subgraphs in achlioptas processes with growing parameter

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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