Matching Orderable and Separable Hypergraphs

TL;DR

This paper investigates the computational complexity of finding perfect matchings in special classes of hypergraphs, showing polynomial algorithms for orderable hypergraphs and NP-completeness for separable hypergraphs when the hyperedge size is at least three.

Contribution

It establishes a clear complexity boundary between orderable and separable hypergraphs regarding perfect matching problems, with new polynomial and NP-complete results.

Findings

Polynomial-time algorithms for perfect matching in orderable hypergraphs for fixed k.

NP-completeness of perfect matching in separable hypergraphs for fixed k ≥ 3.

Orderable hypergraphs form a strict subset of separable hypergraphs.

Abstract

A perfect matching in a hypergraph is a set of edges that partition the set of vertices. We study the complexity of deciding the existence of a perfect matching in orderable and separable hypergraphs. We show that the class of orderable hypergraphs is strictly contained in the class of separable hypergraphs. Accordingly, we show that for each fixed $k$, deciding perfect matching for orderable $k$-hypergraphs is polynomial time doable, but for each fixed $k\geq 3$, it is NP-complete for separable hypergraphs.