On the Random Minimum Spanning Subgraph Problem for Hypergraphs

TL;DR

This paper extends the understanding of minimum spanning structures from graphs to hypergraphs, analyzing how the minimal spanning subgraph behaves under random weights.

Contribution

It generalizes known results about minimum spanning trees in graphs to the more complex setting of hypergraphs, providing new theoretical insights.

Findings

Minimum spanning subgraph weight tends to a constant in hypergraphs

Generalization of graph results to hypergraph setting

Theoretical framework for random hypergraph weights

Abstract

The weight of the minimum spanning tree in a complete weighted graph with random edge weights is a well-known problem. For various classes of distributions, it is proved that the weight of the minimum spanning tree tends to a constant, which can be calculated depending on the distribution. In this paper, we generalise this result to the hypergraphs setting.