Šoltés' hypergraphs
Fuente:
arXiv
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| Auteur principal: | |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916271660990464 |
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| author | Cambie, Stijn |
| author_facet | Cambie, Stijn |
| contents | More than $30$ years ago, Šoltés observed that the total distance of the graph $C_{11}$ does not change by deleting a vertex, and wondered about the existence of other such graphs, called Šoltés graphs. We extend the definition of Šoltés' graphs to Šoltés' hypergraphs, determine all orders for which a Šoltés' hypergraph exists, observe infinitely many uniform Šoltés' hypergraphs, and find the Šoltés' hypergraph with minimum size (spoiler: it is not $C_{11}$). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_01504 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Šoltés' hypergraphs Cambie, Stijn Combinatorics 05C09, 05C12, 05C65 More than $30$ years ago, Šoltés observed that the total distance of the graph $C_{11}$ does not change by deleting a vertex, and wondered about the existence of other such graphs, called Šoltés graphs. We extend the definition of Šoltés' graphs to Šoltés' hypergraphs, determine all orders for which a Šoltés' hypergraph exists, observe infinitely many uniform Šoltés' hypergraphs, and find the Šoltés' hypergraph with minimum size (spoiler: it is not $C_{11}$). |
| title | Šoltés' hypergraphs |
| topic | Combinatorics 05C09, 05C12, 05C65 |
| url | https://arxiv.org/abs/2406.01504 |