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 | |
| 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.