Séminaire

Lovasz and Plummer conjectured a long time ago that the number of perfect matchings in a cubic bridgeless graph on n vertices is exponential with respect to n. Only in 2011, Esperet et al. gave a first proof of it. Ten years later, a young and bright student of a Russian university, Nikita Manuylenko, picked that article as a project paper and managed to improve the bound. I shall present those results. There will be burls and small cuts and long decompositions !