Proportional hypergraph burning

doi:10.4153/S0008414X26102120

Proportional hypergraph burning

2026-03-01

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DOI：10.4153/S0008414X26102120

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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 apply to hypergraphs in both round-based and lazy settings. 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.We obtain bounds on the burning numbers of general hypergraphs, and introduce the concept of the burning distribution, which describes how the burning numbers change as the proportion parameter 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.

Keywords:

Hypergraph theory

design theory

graph burning

graph searching

combinatorial games on graphs

Proportional hypergraph burning

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