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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2403.01001 |
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| _version_ | 1866913983571689472 |
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| author | Burgess, Andrea C. Jones, Caleb W. Pike, David A. |
| author_facet | Burgess, Andrea C. Jones, Caleb W. Pike, David A. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_01001 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Extending Graph Burning to Hypergraphs Burgess, Andrea C. Jones, Caleb W. Pike, David A. Combinatorics 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. |
| title | Extending Graph Burning to Hypergraphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2403.01001 |