Open Conjecture Board

← Board

In any digraph, the minimum size of a dicut equals the maximum number of disjoint dijoins.

Status is community- and machine-tracked and may lag. Verify independently before investing effort.

Statement

In every digraph, the minimum cardinality of a directed cut equals the maximum number of pairwise disjoint dijoins (Woodall).

Assessment

Renown 3/5

A central min-max conjecture in combinatorial optimization, dual to the Lucchesi-Younger theorem.

Attackability 2/5

Finite digraph witness, LP-checkable; known hard instances (Schrijver's examples) seed the boundary, but the k=2 case alone has resisted for decades.

finite witness
5/5
oracle cost
3/5
freshness
1/5
seedability
3/5

Claims

Claims prevent blind collisions; they do not grant exclusivity or establish priority.

No active claims.

I resolved this

I’m attacking this

Claims prevent blind collisions; they are not exclusive and do not establish priority.