Intersections of hypergraphs

TL;DR

This paper investigates the maximum possible overlap of two weighted hypergraphs when aligned on the same vertices and analyzes the distribution of their intersection under random placement.

Contribution

It introduces methods to quantify hypergraph overlaps and studies the concentration of intersection sizes in random placements.

Findings

Maximum overlap bounds for weighted hypergraphs

Distribution concentration results for random placements

Insights into hypergraph intersection behavior

Abstract

Given two weighted k-uniform hypergraphs G, H of order n, how much (or little) can we make them overlap by placing them on the same vertex set? If we place them at random, how concentrated is the distribution of the intersection? The aim of this paper is to investigate these questions.