Combinatorica

, Volume 32, Issue 4, pp 403–424

Perfect matchings in planar cubic graphs

Original Paper

Abstract

A well-known conjecture of Lovász and Plummer from the mid-1970’s, still open, asserts that for every cubic graph G with no cutedge, the number of perfect matchings in G is exponential in |V (G)|. In this paper we prove the conjecture for planar graphs; we prove that if G is a planar cubic graph with no cutedge, then G has at least
$$2^{{{\left| {V(G)} \right|} \mathord{\left/ {\vphantom {{\left| {V(G)} \right|} {655978752}}} \right. \kern-\nulldelimiterspace} {655978752}}}$$
perfect matchings.

Mathematics Subject Classification (2000)

05C70 05C10 

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References

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    T. Fowler: Unique Coloring of Planar Graphs, Ph.D. thesis, Georgia Institute of Technology, 1998.Google Scholar
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    D. Král, J.-S. Sereni and M. Stiebitz: A new lower bound on the number of perfect matchings in cubic graphs, submitted for publication (manuscript 2008).Google Scholar
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Copyright information

© János Bolyai Mathematical Society and Springer Verlag 2012

Authors and Affiliations

  1. 1.Columbia UniversityNew YorkUSA
  2. 2.Princeton UniversityPrincetonUSA

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