{"paper":{"title":"Optimal stability results on color-biased Hamilton cycles","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Mingyuan Rong, Wenchong Chen, Zixiang Xu","submitted_at":"2025-07-23T17:52:43Z","abstract_excerpt":"We investigate Hamilton cycles in edge-colored graphs with \\( r \\) colors, focusing on the notion of color-bias (discrepancy), the maximum deviation from uniform color frequencies along a cycle. Foundational work by Balogh, Csaba, Jing, and Pluh\\'{a}r, and the later generalization by Freschi, Hyde, Lada, and Treglown, as well as an independent work by Gishboliner, Krivelevich, and Michaeli, established that any \\(n\\)-vertex graph with minimum degree exceeding \\( \\frac{(r+1)n}{2r} + \\frac{m}{2}\\) contains a Hamilton cycle with color-bias at least \\(m\\), and characterized the extremal graphs wit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.17739","kind":"arxiv","version":2},"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/2507.17739/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"}