# perfect matching

## Exponentially many perfect matchings in cubic graphs ★★★

**Conjecture**There exists a fixed constant so that every -vertex cubic graph without a cut-edge has at least perfect matchings.

Keywords: cubic; perfect matching

## The intersection of two perfect matchings ★★

**Conjecture**Every bridgeless cubic graph has two perfect matchings , so that does not contain an odd edge-cut.

Keywords: cubic; nowhere-zero flow; perfect matching

## The Berge-Fulkerson conjecture ★★★★

**Conjecture**If is a bridgeless cubic graph, then there exist 6 perfect matchings of with the property that every edge of is contained in exactly two of .

Keywords: cubic; perfect matching