Lukens, Géon (2026) The burning number conjecture (holds asymptotically). Bachelor's Thesis, Mathematics.
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Abstract
The burning number $b(G)$ of a graph $G$ is the smallest number of steps required to burn all vertices of a graph if at every step we start a fire (burn a vertex) and existing fires spread to adjacent vertices. The burning number conjecture of Bonato suggests that $b(G) \leq \lceil \sqrt{n} \rceil$ for any connected finite graph $G$ with $n$ vertices. Norin and Turcotte prove that this conjecture holds, that is $b(G) \leq (1+o(1)) \sqrt{n}$. We explore how this all came to be. This thesis does not present new results, but aim to intuitively explain and clarify the proof of Norin and Turcotte, with expanded explanations of metric trees, cover and probabilistic arguments.
| Item Type: | Thesis (Bachelor's Thesis) |
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| Supervisor name: | Donderwinkel, S.A. and Muller, T. |
| Degree programme: | Mathematics |
| Thesis type: | Bachelor's Thesis |
| Language: | English |
| Date Deposited: | 16 Jan 2026 07:48 |
| Last Modified: | 16 Jan 2026 07:48 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/37208 |
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