Coloring problems on arrangements of pseudolines
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Accesso online: | |
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| _version_ | 1866929248629948416 |
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| author | Roch, Sandro |
| author_facet | Roch, Sandro |
| contents | Arrangements of pseudolines are a widely studied generalization of line arrangements. They are defined as a finite family of infinite curves in the Euclidean plane, any two of which intersect at exactly one point. One can state various related coloring problems depending on the number $n$ of pseudolines. In this article, we show that $n$ colors are sufficient for coloring the crossings avoiding twice the same color on the boundary of any cell, or, alternatively, avoiding twice the same color along any pseudoline. We also study the problem of coloring the pseudolines avoiding monochromatic crossings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_12564 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Coloring problems on arrangements of pseudolines Roch, Sandro Combinatorics Computational Geometry Discrete Mathematics Arrangements of pseudolines are a widely studied generalization of line arrangements. They are defined as a finite family of infinite curves in the Euclidean plane, any two of which intersect at exactly one point. One can state various related coloring problems depending on the number $n$ of pseudolines. In this article, we show that $n$ colors are sufficient for coloring the crossings avoiding twice the same color on the boundary of any cell, or, alternatively, avoiding twice the same color along any pseudoline. We also study the problem of coloring the pseudolines avoiding monochromatic crossings. |
| title | Coloring problems on arrangements of pseudolines |
| topic | Combinatorics Computational Geometry Discrete Mathematics |
| url | https://arxiv.org/abs/2402.12564 |