Ouwejan, Jiske (2026) The Bunkbed Conjecture: Intuition, Counterexamples, and Graph Connectivity. Bachelor's Thesis, Mathematics.
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Abstract
The bunkbed conjecture is a problem in probabilistic graph theory concerning connectivity in random layered graphs. It states that a vertex should be at least as likely to be connected to another vertex in the same layer as to the corresponding vertex in the opposite layer. Despite its intuitive appeal and many positive results for special classes of graphs, the conjecture was disproved in 2024. In this thesis, we introduce the bunkbed construction, discuss the intuition behind the conjecture, review known positive results and recent counterexamples, and presents both numerical experiments and an additional positive result concerning the conjecture.
| 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: | 21 Jul 2026 07:28 |
| Last Modified: | 21 Jul 2026 07:28 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/37456 |
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