| Autor: |
Czerwiński, Sebastian |
| Rok vydání: |
2022 |
| Předmět: |
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| Zdroj: |
Discrete Mathematics & Theoretical Computer Science, vol. 26:2, Graph Theory (July 16, 2024) dmtcs:11101 |
| Druh dokumentu: |
Working Paper |
| DOI: |
10.46298/dmtcs.11101 |
| Popis: |
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 $\Delta$ with $m$ edges. We use the local cut lemma of A. Bernshteyn. |
| Databáze: |
arXiv |
| Externí odkaz: |
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