# Berge, Claude

## Linial-Berge path partition duality ★★★

**Conjecture**The minimum -norm of a path partition on a directed graph is no more than the maximal size of an induced -colorable subgraph.

Keywords: coloring; directed path; partition

## 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