Bounding the Number of Minimal Transversals in Tripartite 3-Uniform Hypergraphs

TL;DR

This paper establishes tight bounds on the number of minimal transversals in tripartite 3-uniform hypergraphs, which are relevant in data applications, by providing precise linear bounds relative to the number of vertices.

Contribution

It introduces tight linear bounds on the number of minimal transversals in tripartite 3-uniform hypergraphs, a class relevant in data-driven applications.

Findings

Lower bound of approximately 1.4977 times the number of vertices

Upper bound of approximately 1.5012 times the number of vertices

Bounds are tight and applicable to data-related hypergraph classes

Abstract

We bound the number of minimal hypergraph transversals that arise in tri-partite 3-uniform hypergraphs, a class commonly found in applications dealing with data. Let H be such a hypergraph on a set of vertices V. We give a lower bound of 1.4977 |V | and an upper bound of 1.5012 |V | .