{"paper":{"title":"Discrepancies of spanning trees in dense graphs","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Adva Mond, Julien Portier, Lawrence Hollom, Lyuben Lichev","submitted_at":"2024-10-22T14:04:33Z","abstract_excerpt":"We address several related problems on combinatorial discrepancy of trees in a setting introduced by Erd\\H{o}s, F\\\"{u}redi, Loebl and S\\'{o}s. Given a fixed tree $T$ on $n$ vertices and an edge-colouring of the complete graph $K_n$, for every colour, we find a copy of $T$ in $K_n$ where the number of edges in that colour significantly exceeds its expected count in a uniformly random embedding. This resolves a problem posed by Erd\\H{o}s, F\\\"{u}redi, Loebl and S\\'{o}s by generalising their work from two to many colours. Furthermore, if $T$ has maximum degree $\\Delta\\leq\\epsilon n$ for sufficient"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.17034","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/2410.17034/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"}