Random lifts of graphs: Perfekt matchings

Nathan Linial; Eyal Rozenman

doi:10.1007/s00493-005-0024-8

Random lifts of graphs: Perfekt matchings

Nathan Linial^*
, Eyal Rozenman

^*Corresponding author for this work

The Rachel and Selim Benin School of Engineering and Computer Science

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

22 Scopus citations

Abstract

We study random lifts of a graph G as defined in [1]. We prove a 0-1 law which states that for every graph G either almost every lift of G has a perfect matching, or almost none of its lifts has a perfect matching. We provide a precise description of this dichotomy. Roughly speaking, the a.s. existence of a perfect matching in the lift depends on the existence of a fractional perfect matching in G. The precise statement appears in Theorem 1.

Original language	English
Pages (from-to)	407-424
Number of pages	18
Journal	Combinatorica
Volume	25
Issue number	4
DOIs	https://doi.org/10.1007/s00493-005-0024-8
State	Published - Jul 2005

Bibliographical note

Funding Information:
* Supported in part by BSF and by the Israeli academy of sciences. 1Graphs in this paper are in fact multigraphs. Multiple edges and loops are allowed, unless otherwise stated. A random lift of a loop on a vertex v is the graph of a random permutation on the fiber of v.

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abstract = "We study random lifts of a graph G as defined in [1]. We prove a 0-1 law which states that for every graph G either almost every lift of G has a perfect matching, or almost none of its lifts has a perfect matching. We provide a precise description of this dichotomy. Roughly speaking, the a.s. existence of a perfect matching in the lift depends on the existence of a fractional perfect matching in G. The precise statement appears in Theorem 1.",

author = "Nathan Linial and Eyal Rozenman",

note = "Funding Information: * Supported in part by BSF and by the Israeli academy of sciences. 1Graphs in this paper are in fact multigraphs. Multiple edges and loops are allowed, unless otherwise stated. A random lift of a loop on a vertex v is the graph of a random permutation on the fiber of v.",

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Random lifts of graphs: Perfekt matchings

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