{"paper":{"title":"Colour-biased Hamilton cycles in randomly perturbed graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Wenchong Chen, Xinbu Cheng, Zhifei Yan","submitted_at":"2025-06-04T17:36:49Z","abstract_excerpt":"Given a graph $G$ and an $r$-edge-colouring $\\chi$ on $E(G)$, a Hamilton cycle $H\\subset G$ is said to have $t$ colour-bias if $H$ contains $n/r+t$ edges of the same colour in $\\chi$. Freschi, Hyde, Lada and Treglown showed every $r$-coloured graph $G$ on $n$ vertices with $\\delta(G)\\geq(r+1)n/2r+t$ contains a Hamilton cycle $H$ with $\\Omega(t)$ colour-bias, generalizing a result of Balogh, Csaba, Jing and Pluh\\'{a}r. In 2022, Gishboliner, Krivelevich and Michaeli proved that the random graph $G(n,m)$ with $m\\geq(1/2+\\varepsilon)n\\log n$ typically admits an $\\Omega(n)$ colour biased Hamilton c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.04189","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/2506.04189/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"}