Eternally surrounding a robber
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866916897045348352 |
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| author | Clarke, Nancy E. Dyer, Danny Kellough, William |
| author_facet | Clarke, Nancy E. Dyer, Danny Kellough, William |
| contents | We introduce the bodyguard problem for graphs. This is a variation of Surrounding Cops and Robber but, in this model, a smallest possible group of bodyguards must surround the president and then maintain this protection indefinitely. We investigate some elementary bounds, then solve this problem for the infinite graph families of complete graphs, wheels, trees, cycles, complete multipartite graphs, and two-dimensional grids. We also examine the problem in more general Cartesian, strong, and lexicographic products. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_10452 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Eternally surrounding a robber Clarke, Nancy E. Dyer, Danny Kellough, William Combinatorics 05C57, 91A43 We introduce the bodyguard problem for graphs. This is a variation of Surrounding Cops and Robber but, in this model, a smallest possible group of bodyguards must surround the president and then maintain this protection indefinitely. We investigate some elementary bounds, then solve this problem for the infinite graph families of complete graphs, wheels, trees, cycles, complete multipartite graphs, and two-dimensional grids. We also examine the problem in more general Cartesian, strong, and lexicographic products. |
| title | Eternally surrounding a robber |
| topic | Combinatorics 05C57, 91A43 |
| url | https://arxiv.org/abs/2408.10452 |