On harmonious coloring of hypergraphs
Sebastian Czerwi\'nski

TL;DR
This paper investigates harmonious colorings of hypergraphs, providing a new proof for an upper bound on the harmonious number using the local cut lemma, which advances understanding of hypergraph colorings.
Contribution
It offers a novel proof of an upper bound on the harmonious number of hypergraphs employing the local cut lemma, enhancing theoretical bounds in hypergraph coloring.
Findings
Established an upper bound h(H)=O(√[k]{k!m}) for the harmonious number.
Applied the local cut lemma of A. Bernshteyn to hypergraph coloring.
Provided a new proof technique for bounds on harmonious colorings.
Abstract
A harmonious coloring of a -uniform hypergraph is a vertex coloring such that no two vertices in the same edge have the same color, and each -element subset of colors appears on at most one edge. The harmonious number is the least number of colors needed for such a coloring. The paper contains a new proof of the upper bound on the harmonious number of hypergraphs of maximum degree with edges. We use the local cut lemma of A. Bernshteyn.
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Taxonomy
TopicsGraph Labeling and Dimension Problems · Limits and Structures in Graph Theory · Nuclear Receptors and Signaling
