A Note on Graph Burning of Path Forests
Graph burning is a natural discrete graph algorithm inspired by the spread of social contagion. Despite its simplicity, some open problems remain steadfastly unsolved, notably the burning number conjecture, which says that every connected graph of order $m^2$ has burning number at most $m$. Earlier,...
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Discrete Mathematics & Theoretical Computer Science
2024-08-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
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| Online Access: | http://dmtcs.episciences.org/12709/pdf |
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| author | Ta Sheng Tan Wen Chean Teh |
| author_facet | Ta Sheng Tan Wen Chean Teh |
| author_sort | Ta Sheng Tan |
| collection | DOAJ |
| description | Graph burning is a natural discrete graph algorithm inspired by the spread of social contagion. Despite its simplicity, some open problems remain steadfastly unsolved, notably the burning number conjecture, which says that every connected graph of order $m^2$ has burning number at most $m$. Earlier, we showed that the conjecture also holds for a path forest, which is disconnected, provided each of its paths is sufficiently long. However, finding the least sufficient length for this to hold turns out to be nontrivial. In this note, we present our initial findings and conjectures that associate the problem to some naturally impossibly burnable path forests. It is noteworthy that our problem can be reformulated as a topic concerning sumset partition of integers. |
| format | Article |
| id | doaj-art-adbdf42eb14c4e758c1de63aa9b4e161 |
| institution | Kabale University |
| issn | 1365-8050 |
| language | English |
| publishDate | 2024-08-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj-art-adbdf42eb14c4e758c1de63aa9b4e1612025-08-20T03:42:37ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80502024-08-01vol. 26:3Discrete Algorithms10.46298/dmtcs.1270912709A Note on Graph Burning of Path ForestsTa Sheng TanWen Chean TehGraph burning is a natural discrete graph algorithm inspired by the spread of social contagion. Despite its simplicity, some open problems remain steadfastly unsolved, notably the burning number conjecture, which says that every connected graph of order $m^2$ has burning number at most $m$. Earlier, we showed that the conjecture also holds for a path forest, which is disconnected, provided each of its paths is sufficiently long. However, finding the least sufficient length for this to hold turns out to be nontrivial. In this note, we present our initial findings and conjectures that associate the problem to some naturally impossibly burnable path forests. It is noteworthy that our problem can be reformulated as a topic concerning sumset partition of integers.http://dmtcs.episciences.org/12709/pdfmathematics - combinatorics05c85, 05a17, 68r10 |
| spellingShingle | Ta Sheng Tan Wen Chean Teh A Note on Graph Burning of Path Forests Discrete Mathematics & Theoretical Computer Science mathematics - combinatorics 05c85, 05a17, 68r10 |
| title | A Note on Graph Burning of Path Forests |
| title_full | A Note on Graph Burning of Path Forests |
| title_fullStr | A Note on Graph Burning of Path Forests |
| title_full_unstemmed | A Note on Graph Burning of Path Forests |
| title_short | A Note on Graph Burning of Path Forests |
| title_sort | note on graph burning of path forests |
| topic | mathematics - combinatorics 05c85, 05a17, 68r10 |
| url | http://dmtcs.episciences.org/12709/pdf |
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