Random lifts of graphs: Perfekt matchings

Nathan Linial*, Eyal Rozenman

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

21 Scopus citations


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 languageAmerican English
Pages (from-to)407-424
Number of pages18
Issue number4
StatePublished - 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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