Seeing is not believing in limited visibility cops and robbers
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909670434668544 |
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| author | Bašić, Bojan Davies, Alfie Džuklevski, Aleksa Gvozdić, Strahinja Mogge, Yannick |
| author_facet | Bašić, Bojan Davies, Alfie Džuklevski, Aleksa Gvozdić, Strahinja Mogge, Yannick |
| contents | We consider the model of limited visibility Cops and Robbers, where the cops can only see within their $l$-neighbourhood. We prove that the number of cops needed to see the robber can be arbitrarily smaller than the number needed to capture the robber, answering an open question from the literature. We then consider how close we can get to seeing the robber when we do not have enough cops, along with a probabilistic interpretation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_00941 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Seeing is not believing in limited visibility cops and robbers Bašić, Bojan Davies, Alfie Džuklevski, Aleksa Gvozdić, Strahinja Mogge, Yannick Combinatorics Discrete Mathematics 49N75 We consider the model of limited visibility Cops and Robbers, where the cops can only see within their $l$-neighbourhood. We prove that the number of cops needed to see the robber can be arbitrarily smaller than the number needed to capture the robber, answering an open question from the literature. We then consider how close we can get to seeing the robber when we do not have enough cops, along with a probabilistic interpretation. |
| title | Seeing is not believing in limited visibility cops and robbers |
| topic | Combinatorics Discrete Mathematics 49N75 |
| url | https://arxiv.org/abs/2507.00941 |