Proportion-Based Hypergraph Burning

TL;DR

This paper introduces a proportion-based hypergraph burning model that extends influence spread modeling, providing new theoretical bounds, the concept of burning distribution, and computational insights into hypergraph automorphisms.

Contribution

It proposes a novel hypergraph burning variant using a fixed proportion rule, develops bounds for general hypergraphs, and introduces the burning distribution concept.

Findings

Bounds applicable to general hypergraphs

Introduction of the burning distribution concept

Correlation between automorphism group size and burning number

Abstract

Graph burning is a discrete process that models the spread of influence through a network using a fire as a proxy for the type of influence being spread. This process was recently extended to hypergraphs. We introduce a variant of hypergraph burning that uses an alternative propagation rule for how the fire spreads - if some fixed proportion of vertices are on fire in a hyperedge, then in the next round the entire hyperedge catches fire. This new variant has more potential for applications than the original model, and it is similarly viable for obtaining deep theoretical results. We obtain bounds which apply to general hypergraphs, and introduce the concept of the burning distribution, which describes how the model changes as the proportion ranges over (0,1). We also obtain computational results which suggest there is a strong correlation between the automorphism group order and the lazy burning number of a balanced incomplete block design.