Cuts, Cats, and Complete Graphs
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916403936755712 |
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| author | Ashmore, Rylo Dyer, Danny Marbach, Trent Milley, Rebecca |
| author_facet | Ashmore, Rylo Dyer, Danny Marbach, Trent Milley, Rebecca |
| contents | We introduce the game of Cat Herding, where an omnipresent herder slowly cuts down a graph until an evasive cat player has nowhere to go. The number of cuts made is the score of a game, and we study the score under optimal play. In this paper, we begin by deriving some general results, and then we determine the precise cat number for paths, cycles, stars, and wheels. Finally, we identify an optimal Cat and Herder strategy on complete graphs, while providing both a recurrence and closed form for $cat(K_n)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_13685 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Cuts, Cats, and Complete Graphs Ashmore, Rylo Dyer, Danny Marbach, Trent Milley, Rebecca Combinatorics 05C57 (Primary) 91A24, 91A46, 68R05 (Secondary) We introduce the game of Cat Herding, where an omnipresent herder slowly cuts down a graph until an evasive cat player has nowhere to go. The number of cuts made is the score of a game, and we study the score under optimal play. In this paper, we begin by deriving some general results, and then we determine the precise cat number for paths, cycles, stars, and wheels. Finally, we identify an optimal Cat and Herder strategy on complete graphs, while providing both a recurrence and closed form for $cat(K_n)$. |
| title | Cuts, Cats, and Complete Graphs |
| topic | Combinatorics 05C57 (Primary) 91A24, 91A46, 68R05 (Secondary) |
| url | https://arxiv.org/abs/2409.13685 |