dissertation · Memorial University Research Repository (Memorial University) · 2023
Hypergraph burning
Jones, Caleb
Cited by 0Open access
Abstract
Graph burning is a combinatorial game or process that models the spread of in \nuence \nthroughout a network. We introduce a generalization of graph burning which applies to \nhypergraphs. One of our key results is that arbitrary hypergraphs do not satisfy a bound \nanalogous to the one in the Burning Number Conjecture. We also introduce a variant called \n\\lazy" hypergraph burning, along with a new parameter, the lazy burning number. Interestingly, \nlazily burning a graph is trivial, while lazily burning a hypergraph can be quite \ncomplicated. Moreover, the lazy burning model is a useful tool for analyzing the roundbased \nmodel. We obtain bounds on the burning number and lazy burning number of a \nhypergraph in terms of its parameters, as well as stronger bounds that apply to Steiner \ntriple systems. We also discuss the complexity of both the round-based and lazy models. \nFinally, we introduce two further variants of (lazy) hypergraph burning.
Cite this paper
Jones, C. (2023). Hypergraph burning. Memorial University Research Repository (Memorial University).
Jones, Caleb. “Hypergraph burning.” Memorial University Research Repository (Memorial University), 2023.
Jones, Caleb. 2023. “Hypergraph burning.” Memorial University Research Repository (Memorial University).
Jones, C. (2023) ‘Hypergraph burning’, Memorial University Research Repository (Memorial University).
@phdthesis{jones2023hypergraph,
title = {{Hypergraph burning}},
author = {Jones, Caleb},
school = {Memorial University Research Repository (Memorial University)},
year = {2023}
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