{"paper":{"title":"\\v{S}olt\\'es' hypergraphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Stijn Cambie","submitted_at":"2024-06-03T16:31:25Z","abstract_excerpt":"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 $C_{11}$)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.01504","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2406.01504/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}