Testing the max-flow min-cut property and the replication conjecture (opens in new tab)

The replication conjecture [Conforti and Cornu\'{e}jols, 1993] states that every clutter with the packing property has the MFMC property. If true, this conjecture would have far-reaching consequences from integer programming and combinatorial optimization to commutative algebra. In this paper, we set out to verify the conjecture for the cuboid of a set-system in which the Hamming graph induced on the infeasible points has degree at most $\delt...