Fractional Covers of Hypergraphs with Bounded Multi-Intersection

TL;DR

This paper generalizes conditions for fractional edge covers in hypergraphs with bounded multi-intersection, enabling improved analysis of fractional hypertree width and vertex covers.

Contribution

It introduces a unified framework that bounds the support size of fractional covers in hypergraphs with bounded multi-intersection, extending tractability results.

Findings

Bounded support size of fractional edge covers in hypergraphs with multi-intersection.

Extended tractability for fractional hypertree width verification.

Results applicable to fractional vertex covers.

Abstract

Fractional (hyper-)graph theory is concerned with the specific problems that arise when fractional analogues of otherwise integer-valued (hyper-)graph invariants are considered. The focus of this paper is on fractional edge covers of hypergraphs. Our main technical result generalizes and unifies previous conditions under which the size of the support of fractional edge covers is bounded independently of the size of the hypergraph itself. This allows us to extend previous tractability results for checking if the fractional hypertree width of a given hypergraph is $\leq k$ for some constant $k$. We also show how our results translate to fractional vertex covers.