{"paper":{"title":"Universality for bounded degree spanning trees in randomly perturbed graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jie Han, Julia B\\\"ottcher, Olaf Parczyk, Richard Montgomery, Yoshiharu Kohayakawa, Yury Person","submitted_at":"2018-02-13T16:22:32Z","abstract_excerpt":"We solve a problem of Krivelevich, Kwan and Sudakov [SIAM Journal on Discrete Mathematics 31 (2017), 155-171] concerning the threshold for the containment of all bounded degree spanning trees in the model of randomly perturbed dense graphs. More precisely, we show that, if we start with a dense graph $G_\\alpha$ on $n$ vertices with $\\delta(G_\\alpha)\\ge \\alpha n$ for $\\alpha>0$ and we add to it the binomial random graph $G(n,C/n)$, then with high probability the graph $G_\\alpha\\cup G(n,C/n)$ contains copies of all spanning trees with maximum degree at most $\\Delta$ simultaneously, where $C$ dep"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.04707","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":""},"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"}