Extending Graph Burning to Hypergraphs

• Main Authors: Burgess, Andrea C, Jones, Caleb W, Pike, David A
• Format: Journal Article
• Language: English
• Published: 01-03-2024
• Subjects: Mathematics - Combinatorics
• DOI: 10.48550/arxiv.2403.01001

Graph burning is a round-based game or process that discretely models the
spread of influence throughout a network. We introduce a generalization of
graph burning which applies to hypergraphs, as well as a variant called
''lazy'' hypergraph burning. Interestingly, lazily burning a graph is trivial,
while lazily burning a hypergraph can be quite complicated. Moreover, the lazy
burning model is a useful tool for analyzing the round-based model. One of our
key results is that arbitrary hypergraphs do not satisfy a bound analogous to
the one in the Burning Number Conjecture for graphs. We also obtain bounds on
the burning number and lazy burning number of a hypergraph in terms of its
parameters, and present several open problems in the field of (lazy) hypergraph
burning.