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Combinatorica

, Volume 25, Issue 4, pp 407–424 | Cite as

Random Lifts Of Graphs: Perfect Matchings

  • Nathan Linial*Email author
  • Eyal Rozenman
Original Paper

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.

Mathematics Subject Classification (2000):

05C80 05C70 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  1. 1.Institute of Computer ScienceHebrew UniversityJerusalem 91904Israel
  2. 2.Institute of Computer ScienceHebrew UniversityJerusalem 91904Israel

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