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Opis: 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.
Ključne besede: Combinatorial games on graphs, pursuit-evasion, graph searching, graph burning, hypergraph theory
Objavljeno v RUP: 18.08.2026; Ogledov: 498; Prenosov: 9
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