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Approximately Packing Dijoins Via Nowhere-Zero Flows (SIMONS-TCS-ML)

Professor

33:46·2026·research level

R Ravi explores Woodall's conjecture on dijoins, proving that digraphs with minimum dicut size $\tau$ contain $\lfloor \tau/k \rfloor$ disjoint dijoins if the underlying graph has a nowhere-zero k-flow.

R Ravi (Carnegie Mellon University)

The Role of TCS in Modern Machine Learning

In a digraph, a dicut is a cut where all the arcs cross in one direction. A dijoin is a subset of arcs that intersects each dicut. Woodall conjectured in 1976 that in every digraph, the minimum size of a dicut equals to the maximum number of disjoint dijoins. By building connections with nowhere-zero k-flows, we prove that every digraph with minimum dicut size $\tau$ contains $\lfloor \tau/k \rfloor$ disjoint dijoins if the underlying undirected graph admits a nowhere-zero k-flow.

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