Sebastian Czerwiński - On harmonious coloring of hypergraphs

dmtcs:11101 - Discrete Mathematics & Theoretical Computer Science, July 16, 2024, vol. 26:2 - https://doi.org/10.46298/dmtcs.11101
On harmonious coloring of hypergraphsArticle

Authors: Sebastian Czerwiński

    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.


    Volume: vol. 26:2
    Section: Graph Theory
    Published on: July 16, 2024
    Accepted on: April 5, 2024
    Submitted on: March 21, 2023
    Keywords: Mathematics - Combinatorics,05C15

    Publications

    References
    Czerwiński, S. (2023). On harmonious coloring of hypergraphs. ArXiv. 10.48550/ARXIV.2301.00302

    Consultation statistics

    This page has been seen 183 times.
    This article's PDF has been downloaded 69 times.