{"paper":{"title":"Bounds of a number of leaves of spanning trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Anton Bankevich, Dmitri Karpov","submitted_at":"2011-11-14T16:19:56Z","abstract_excerpt":"We prove that every connected graph with $s$ vertices of degree not 2 has a spanning tree with at least ${1\\over 4}(s-2)+2$ leaves.\n  Let $G$ be a be a connected graph of girth $g$ with $v>1$ vertices. Let maximal chain of successively adjacent vertices of degree 2 in the graph $G$ does not exceed $k\\ge 1$. We prove that $G$ has a spanning tree with at least $\\alpha_{g,k}(v(G)-k-2)+2$ leaves, where $\\alpha_{g,k}= {[{g+1\\over2}]\\over [{g+1\\over2}](k+3)+1}$ for $k<g-2$; $\\alpha_{g,k}= {g-2\\over (g-1)(k+2)}$ for $k\\ge g-2$.\n  We present infinite series of examples showing that all these bounds ar"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.3266","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"}