Moving through Cartesian products, coronas and joins in general position
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arXiv
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| Auteurs principaux: | , , , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908594952208384 |
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| author | Klavžar, Sandi Krishnakumar, Aditi Kuziak, Dorota Shallcross, Ethan Tuite, James Yero, Ismael G. |
| author_facet | Klavžar, Sandi Krishnakumar, Aditi Kuziak, Dorota Shallcross, Ethan Tuite, James Yero, Ismael G. |
| contents | The general position problem asks for large sets of vertices such that no three vertices of the set lie on a common shortest path. Recently a dynamic version of this problem was defined, called the \emph{mobile general position problem}, in which a collection of robots must visit all the vertices of the graph whilst remaining in general position. In this paper we investigate this problem in the context of Cartesian products, corona products and joins, giving upper and lower bounds for general graphs and exact values for families including grids, cylinders, Hamming graphs and prisms of trees. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_00535 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Moving through Cartesian products, coronas and joins in general position Klavžar, Sandi Krishnakumar, Aditi Kuziak, Dorota Shallcross, Ethan Tuite, James Yero, Ismael G. Combinatorics 05C12, 05C69, 05C76 The general position problem asks for large sets of vertices such that no three vertices of the set lie on a common shortest path. Recently a dynamic version of this problem was defined, called the \emph{mobile general position problem}, in which a collection of robots must visit all the vertices of the graph whilst remaining in general position. In this paper we investigate this problem in the context of Cartesian products, corona products and joins, giving upper and lower bounds for general graphs and exact values for families including grids, cylinders, Hamming graphs and prisms of trees. |
| title | Moving through Cartesian products, coronas and joins in general position |
| topic | Combinatorics 05C12, 05C69, 05C76 |
| url | https://arxiv.org/abs/2505.00535 |