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arXiv · 2510.25043

Hedgegraph Polymatroids

Karthekeyan Chandrasekaran·Chandra Chekuri·Weihang Wang·Weihao Zhu
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Abstract

Graphs and hypergraphs combine expressive modeling power with algorithmic efficiency for a wide range of applications. Hedgegraphs generalize hypergraphs further by grouping hyperedges under a color/hedge. This allows hedgegraphs to model dependencies between hyperedges and leads to several applications. However, it poses algorithmic challenges. In particular, the cut function is not submodular, which has been a barrier to algorithms for connectivity. In this work, we introduce two alternative partition-based measures of connectivity in hedgegraphs and study their structural and algorithmic aspects. Instead of the cut function, we investigate a polymatroid associated with hedgegraphs. The polymatroidal lens leads to new tractability results as well as insightful generalizations of classical results on graphs and hypergraphs.

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Karthekeyan Chandrasekaran, Chandra Chekuri, Weihang Wang, Weihao Zhu. 2025-10-29. Hedgegraph Polymatroids. https://arxiv.org/abs/2510.25043

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