On harmonious coloring of hypergraphs
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2022
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866916347469889536 |
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| author | Czerwiński, Sebastian |
| author_facet | Czerwiński, Sebastian |
| contents | A harmonious coloring of a $k$-uniform hypergraph $H$ is a vertex coloring such that no two vertices in the same edge have the same color, and each $k$-element subset of colors appears on at most one edge. The harmonious number $h(H)$ is the least number of colors needed for such a coloring.
The paper contains a new proof of the upper bound $h(H)=O(\sqrt[k]{k!m})$ on the harmonious number of hypergraphs of maximum degree $Δ$ with $m$ edges. We use the local cut lemma of A. Bernshteyn. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_00302 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On harmonious coloring of hypergraphs Czerwiński, Sebastian Combinatorics 05C15 A harmonious coloring of a $k$-uniform hypergraph $H$ is a vertex coloring such that no two vertices in the same edge have the same color, and each $k$-element subset of colors appears on at most one edge. The harmonious number $h(H)$ is the least number of colors needed for such a coloring. The paper contains a new proof of the upper bound $h(H)=O(\sqrt[k]{k!m})$ on the harmonious number of hypergraphs of maximum degree $Δ$ with $m$ edges. We use the local cut lemma of A. Bernshteyn. |
| title | On harmonious coloring of hypergraphs |
| topic | Combinatorics 05C15 |
| url | https://arxiv.org/abs/2301.00302 |