| Title: | Extending graph burning to hypergraphs |
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| Authors: | ID Burgess, Andrea C. (Author)
ID Jones, Caleb W. (Author)
ID Pike, David A. (Author) |
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| Files: |  AMC_Burgess,_Jones,_Pike_2026.pdf (413,95 KB)
MD5: 6C00EF8351AA6993F9D15AC2FD332248
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| Language: | English |
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| Work type: | Article |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: | ZUP - University of Primorska Press
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| Abstract: | 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. |
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| Keywords: | Combinatorial games on graphs, pursuit-evasion, graph searching, graph burning, hypergraph theory |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 18.06.2026 |
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| Publisher: | Založba Univerze na Primorskem |
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| Year of publishing: | 2026 |
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| Number of pages: | 23 str. |
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| Numbering: | Vol. 26, no. 3, [article no.] P3.07 |
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| PID: | 20.500.12556/RUP-23517  |
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| UDC: | 51 |
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| eISSN: | 1855-3974 |
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| DOI: | 10.26493/1855-3974.3451.46f |
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| Publication date in RUP: | 18.08.2026 |
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| Views: | 24 |
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| Downloads: | 0 |
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