The palette index of the Cartesian product of paths, cycles and regular graphs
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917889790967808 |
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| author | Vesel, Aleksander |
| author_facet | Vesel, Aleksander |
| contents | The palette of a vertex v in a graph G is the set of colors assigned to the edges incident to v. The palette index of G is the minimum number of distinct palettes among the vertices, taken over all proper edge colorings of G. This paper presents results on the palette index of the Cartesian product $G \Box H$, where one of the factor graphs is a path or a cycle. Additionally, it provides exact results and bounds on the palette index of the Cartesian product of two graphs, where one factor graph is isomorphic to a regular or class 1 nearly regular graph. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_06569 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The palette index of the Cartesian product of paths, cycles and regular graphs Vesel, Aleksander Combinatorics The palette of a vertex v in a graph G is the set of colors assigned to the edges incident to v. The palette index of G is the minimum number of distinct palettes among the vertices, taken over all proper edge colorings of G. This paper presents results on the palette index of the Cartesian product $G \Box H$, where one of the factor graphs is a path or a cycle. Additionally, it provides exact results and bounds on the palette index of the Cartesian product of two graphs, where one factor graph is isomorphic to a regular or class 1 nearly regular graph. |
| title | The palette index of the Cartesian product of paths, cycles and regular graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2501.06569 |