Geodesic
On harmonious coloring of hypergraphs
Discrete mathematics & theoretical computer science, Tome 26 (2024) no. 2.

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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.
DOI : 10.46298/dmtcs.11101
Classification : 05C15, 05C65 
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Czerwiński, Sebastian. On harmonious coloring of hypergraphs. Discrete mathematics & theoretical computer science, Tome 26 (2024) no. 2. doi : 10.46298/dmtcs.11101. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.11101/

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