, Volume 32, Issue 4, pp 403–424

Perfect matchings in planar cubic graphs

Original Paper

DOI: 10.1007/s00493-012-2660-9

Cite this article as:
Chudnovsky, M. & Seymour, P. Combinatorica (2012) 32: 403. doi:10.1007/s00493-012-2660-9


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 

Copyright information

© János Bolyai Mathematical Society and Springer Verlag 2012

Authors and Affiliations

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

Personalised recommendations