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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.04923 |
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| _version_ | 1866909437282746368 |
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| author | Burgess, Andrea Dyer, Danny Farahani, Mozhgan |
| author_facet | Burgess, Andrea Dyer, Danny Farahani, Mozhgan |
| contents | The deduction game is a variation of the game of cops and robber on graphs in which searchers must capture an invisible evader in at most one move. Searchers know each others' initial locations, but can only communicate if they are on the same vertex. Thus, searchers must deduce other searchers' movement and move accordingly. We introduce the deduction number and study it for various classes of graphs. We provide upper bounds for the deduction number of the Cartesian product of graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_04923 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An introduction to the deduction number Burgess, Andrea Dyer, Danny Farahani, Mozhgan Combinatorics 05C57 The deduction game is a variation of the game of cops and robber on graphs in which searchers must capture an invisible evader in at most one move. Searchers know each others' initial locations, but can only communicate if they are on the same vertex. Thus, searchers must deduce other searchers' movement and move accordingly. We introduce the deduction number and study it for various classes of graphs. We provide upper bounds for the deduction number of the Cartesian product of graphs. |
| title | An introduction to the deduction number |
| topic | Combinatorics 05C57 |
| url | https://arxiv.org/abs/2406.04923 |