Cops and robbers on chess graphs
Fuente:
arXiv
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| Autori principali: | , , , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
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| _version_ | 1866908554692132864 |
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| author | Ambrose, Sally Angelone, Evan Chen, Jacob Ma, Daniel Miguel, Arturo Ortiz San Watanabe, Wraven Whitcomb, Stephen Wu, Shanghao |
| author_facet | Ambrose, Sally Angelone, Evan Chen, Jacob Ma, Daniel Miguel, Arturo Ortiz San Watanabe, Wraven Whitcomb, Stephen Wu, Shanghao |
| contents | Cops and robbers is a pursuit-evasion game played on graphs. We completely classify the cop numbers for $n \times n$ knight graphs and queen graphs. This completes the classification of the cop numbers for all $n \times n$ classical chess graphs. As a corollary, we resolve an open problem about the monotonicity of $c$($\mathcal{Q}_n$). Moreover, we introduce \emph{royal graphs}, a generalization of chess graphs for arbitrary piece movements, which models real-life movement constraints. We give results on the cop numbers for these families. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_18516 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Cops and robbers on chess graphs Ambrose, Sally Angelone, Evan Chen, Jacob Ma, Daniel Miguel, Arturo Ortiz San Watanabe, Wraven Whitcomb, Stephen Wu, Shanghao Combinatorics 2020 MSC 49N75 (Primary), 05C57, 91A24 (Secondary) Cops and robbers is a pursuit-evasion game played on graphs. We completely classify the cop numbers for $n \times n$ knight graphs and queen graphs. This completes the classification of the cop numbers for all $n \times n$ classical chess graphs. As a corollary, we resolve an open problem about the monotonicity of $c$($\mathcal{Q}_n$). Moreover, we introduce \emph{royal graphs}, a generalization of chess graphs for arbitrary piece movements, which models real-life movement constraints. We give results on the cop numbers for these families. |
| title | Cops and robbers on chess graphs |
| topic | Combinatorics 2020 MSC 49N75 (Primary), 05C57, 91A24 (Secondary) |
| url | https://arxiv.org/abs/2509.18516 |