Tan, Ta Sheng and Teh, Wen Chean (2024) A note on graph burning of path forests. Discrete Mathematics and Theoretical Computer Science, 26 (3). p. 1. ISSN 1462-7264,
Full text not available from this repository.Abstract
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 m2 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.
| Item Type: | Article |
|---|---|
| Funders: | Malaysian Ministry of Higher Education for Fundamental Research Grant Scheme (FRGS/1/2023/STG06/USM/02/7) |
| Uncontrolled Keywords: | discrete graph algorithm; burning number conjecture; spread of social contagion; sumset partition of integers; well-burnable |
| Subjects: | Q Science > QA Mathematics |
| Divisions: | Faculty of Science > Institute of Mathematical Sciences |
| Depositing User: | Ms. Juhaida Abd Rahim |
| Date Deposited: | 28 Nov 2024 04:26 |
| Last Modified: | 28 Nov 2024 04:26 |
| URI: | http://eprints.um.edu.my/id/eprint/47119 |
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