{"paper":{"title":"A complete $t$-intersection theorem for families of spanning trees","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Andrey Kupavskii, Elizaveta Iarovikova","submitted_at":"2025-07-23T20:23:34Z","abstract_excerpt":"Let $\\mathcal T_n$ denote the set of all labelled spanning trees of $K_n$. A family $\\mathcal F \\subset \\mathcal T_n$ is $t$-intersecting if for all $A, B \\in \\mathcal F$ the trees $A$ and $B$ share at least $t$ edges. In this paper, we determine for $n>n_0$ the size of the largest $t$-intersecting family $\\mathcal F\\subset \\mathcal T_n$ for all meaningful values of $t$ ($t\\le n-1$). This result is a rare instance when a complete $t$-intersection theorem for a given type of structures is known."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.17913","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/2507.17913/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"}