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arXiv · 2506.07511

Uniform Šoltés' hypergraphs and Šoltés' weighted graphs

Stijn Cambie·Ajay Tiwari
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Abstract

A Šoltés' hypergraph is a hypergraph for which the removal of any of its vertices does not change its total distance. We prove that every uniform Šoltés' hypergraph has order at least $10$, there exist uniform Šoltés' hypergraphs for almost every order or uniformity, and there exist a non-regular uniform Šoltés' hypergraph. By also providing infinitely many weighted Šoltés' graphs, we conclude that Šoltés' problem can be answered positively for the most natural generalisations of graphs.

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BibTeXRIS

Stijn Cambie, Ajay Tiwari. 2025-06-09. Uniform Šoltés' hypergraphs and Šoltés' weighted graphs. https://arxiv.org/abs/2506.07511

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