{"paper":{"title":"Spanning tree with lower bound on the degrees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Zolt\\'an Kir\\'aly","submitted_at":"2017-10-19T11:17:27Z","abstract_excerpt":"We concentrate on some recent results of Egawa and Ozeki [J. Graph Theory, 2015 and Combinatorica, 2014], and He et al. [J. Graph Theory, 2002]. We give shorter proofs and polynomial time algorithms as well.\n  We present two new proofs for the sufficient condition for having a spanning tree with prescribed lower bounds on the degrees, achieved recently by Egawa and Ozeki. The first one is a natural proof using induction, and the second one is a simple reduction to the theorem of Lov\\'asz. Using an algorithm of Frank we show that the condition of the theorem can be checked in time $O(m\\sqrt{n})"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.07089","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":""},"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"}