2 papers
math.CO2026
Cut Conditions, Integrality, and Obstructions for Directed Multiflows
Srinwanti Debgupta, Martin Skutella, Philipp Warode
In contrast to the max-flow/min-cut theorem for single-commodity flows, the cut condition is necessary but not sufficient for the existence of directed multiflows, even with only t…
math.CO2024
Integer and Unsplittable Multiflows in Series-Parallel Digraphs
Mohammed Majthoub Almoghrabi, Martin Skutella, Philipp Warode
An unsplittable multiflow routes the demand of each commodity along a single path from its source to its sink node. As our main result, we prove that in series-parallel digraphs, a…