Title: Berge Conjecture and related problems
Speaker: Roman Nedela (University of West Bohemia)

Long term open Berge conjecture claims that every bridgeless cubic graph G admits a set of at most five perfect matchings covering the edges of G. Berge conjecture trivially holds for 3-edge-colourable cubic graphs. Thus it makes sense to consider it just for snarks.

In the first part of my talk I will survey some new results related to the Berge conjecture. In the second part I will consider Berge conjecture for a class of snarks which admit a 2-factor consisting of two odd cycles. I will show a technique which may help to prove that such graphs, with the exception of Petersen graph, have perfect matching index four.