Bicolored point sets admitting non-crossing alternating Hamiltonian paths
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866913307254849536 |
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| author | Soukup, Jan |
| author_facet | Soukup, Jan |
| contents | Consider a bicolored point set $P$ in general position in the plane consisting of $n$ blue and $n$ red points. We show that if a subset of the red points forms the vertices of a convex polygon separating the blue points, lying inside the polygon, from the remaining red points, lying outside the polygon, then the points of $P$ can be connected by non-crossing straight-line segments so that the resulting graph is a properly colored closed Hamiltonian path. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_06105 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Bicolored point sets admitting non-crossing alternating Hamiltonian paths Soukup, Jan Combinatorics 05C10 Consider a bicolored point set $P$ in general position in the plane consisting of $n$ blue and $n$ red points. We show that if a subset of the red points forms the vertices of a convex polygon separating the blue points, lying inside the polygon, from the remaining red points, lying outside the polygon, then the points of $P$ can be connected by non-crossing straight-line segments so that the resulting graph is a properly colored closed Hamiltonian path. |
| title | Bicolored point sets admitting non-crossing alternating Hamiltonian paths |
| topic | Combinatorics 05C10 |
| url | https://arxiv.org/abs/2404.06105 |