A new lower bound on the number of perfect matchings in cubic graphs

Daniel Král' (1) , Jean-Sébastien Sereni (2, 3) , Michael Stiebitz (4)

1 ITI - Institut teoretické informatiky
2 KAM - Department of Applied Mathematics (KAM)
3 LIAFA - Laboratoire d'informatique Algorithmique : Fondements et Applications
4 Institute of Mathematics - Technical University of Ilmenau

We prove that every n-vertex cubic bridgeless graph has at least n/2 perfect matchings and give a list of all 17 such graphs that have less than n/2+2 perfect matchings.

Mots clés: perfect matching; cubic graph; brick and brace decomposition; perfect matching polytope

Domaines: Mathématique discrète [cs.DM]

Daniel Král', Jean-Sébastien Sereni, Michael Stiebitz. A new lower bound on the number of perfect matchings in cubic graphs. SIAM Journal on Discrete Mathematics, 2009, 23 (3), pp.1465--1483. ⟨10.1137/080723843⟩. ⟨hal-00487173⟩