{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/soltes-hypergraphs","title":"Šoltés' hypergraphs","arxiv_id":"2406.01504","date":"2024-06-03","proceeding":null,"authors":["Stijn Cambie"],"abstract":"More than $30$ years ago, \\v{S}olt\\'es 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 \\v{S}olt\\'es graphs. We extend the definition of \\v{S}olt\\'es' graphs to \\v{S}olt\\'es' hypergraphs, determine all orders for which a \\v{S}olt\\'es' hypergraph exists, observe infinitely many uniform \\v{S}olt\\'es' hypergraphs, and find the \\v{S}olt\\'es' hypergraph with minimum size (spoiler: it is not $C_{11}$).","url_abs":"https://arxiv.org/abs/2406.01504v1","url_pdf":"https://arxiv.org/pdf/2406.01504v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"soltes-hypergraphs","repo_url":"https://github.com/stijncambie/soltes","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}