Uniform Šoltés' hypergraphs and Šoltés' weighted graphs
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866913885148151808 |
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| author | Cambie, Stijn Tiwari, Ajay |
| author_facet | Cambie, Stijn Tiwari, Ajay |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_07511 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Uniform Šoltés' hypergraphs and Šoltés' weighted graphs Cambie, Stijn Tiwari, Ajay Combinatorics 05C09, 05C12, 05C22, 05C65 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. |
| title | Uniform Šoltés' hypergraphs and Šoltés' weighted graphs |
| topic | Combinatorics 05C09, 05C12, 05C22, 05C65 |
| url | https://arxiv.org/abs/2506.07511 |