Probabilistic Games on Graphs, Random Walks, and Resistance Distances
| Thesis title in Czech: | Pravděpodobnostní hry na grafech, náhodné procházky a rezistenční vzdálenosti |
|---|---|
| Thesis title in English: | Probabilistic Games on Graphs, Random Walks, and Resistance Distances |
| Key words: | Markovův řetězec|pravděpodobnostní počítadlo|Pass the Buck|rezistenční vzdálenost|hyperkrychle|Fibonacciho čísla|konvoluce|duely|chip- firing|arborescence|spojení grafů|Čebyševovy polynomy|Kemenyho konstanta |
| English key words: | Markov chain|probabilistic abacus|Pass the Buck|resistance distance|hypercube|Fibonacci numbers|convolution|duels|chip-firing|arborescences|graph join|Chebyshev polynomials|Kemeny’s constant |
| Academic year of topic announcement: | 2021/2022 |
| Thesis type: | dissertation |
| Thesis language: | angličtina |
| Department: | Department of Mathematics Education (32-KDM) |
| Supervisor: | doc. RNDr. Antonín Slavík, Ph.D., DSc. |
| Author: | hidden - assigned and confirmed by the Study Dept. |
| Date of registration: | 01.09.2021 |
| Date of assignment: | 01.09.2021 |
| Confirmed by Study dept. on: | 14.09.2021 |
| Date and time of defence: | 20.05.2026 14:00 |
| Date of electronic submission: | 19.03.2026 |
| Opponents: | prof. RNDr. Michal Křížek, DrSc. |
| prof. RNDr. Petr Stehlík, Ph.D. | |
| Guidelines |
| Cílem disertační práce bude studovat vybrané matematické hry na grafech a zamýšlet se nad jejich modifikacemi. Pozornost bude zaměřena na herní strategie, asymptotické chování her a další otázky. |
| References |
| - Anthony Bonato, Jeannette Janssen, Elham Roshanbin: How to burn a graph, Internet Mathematics 12 (2016), 85–100
- Ta Sheng Tan, Wen Chean Teh: Graph burning: Tight bounds on the burning numbers of path forests and spiders, Applied Mathematics and Computation 385 (2020), 125447 - Anthony Bonato, Richard J. Nowakowski: The Game of Cops and Robbers on Graphs, American Mathematical Society, 2011 - Brendan W. Sullivan, Nikolas Townsend, Mikayla L. Werzanski: An Introduction to Lazy Cops and Robbers on Graphs, The College Mathematics Journal 48 (2017), 322-333 - Steve Butler, Mohammad T. Hajiaghayi, Robert D. Kleinberg, Tom Leighton: Hat Guessing Games, Siam J. Discrete Math. 22 (2008), 592–605 - C. Duffy, T.F. Lidbetter, M.E. Messinger, R.J. Nowakowski: A Variation on Chip-Firing: the diffusion game, Discrete Mathematics and Theoretical Computer Science 20 (2018), #4 - Glenn Iba, James Tanton: Candy Sharing, The American Mathematical Monthly 110 (2003), 25-35 - Grant Cairns: Equitable Candy Sharing, The American Mathematical Monthly 124 (2017), 518-526 |