{"paper":{"title":"An improved error term for minimum H-decompositions of graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Julia B\\\"ottcher, Peter Allen, Yury Person","submitted_at":"2011-09-12T19:07:55Z","abstract_excerpt":"We consider partitions of the edge set of a graph G into copies of a fixed graph H and single edges. Let \\phi_H(n) denote the minimum number p such that any n-vertex G admits such a partition with at most p parts. We show that \\phi_H(n)=ex(n,K_r)+\\Theta(biex(n,H)) for \\chi(H)>2, where biex(n,H) is the extremal number of the decomposition family of H. Since biex(n,H)=O(n^{2-\\gamma}) for some \\gamma>0 this improves on the bound \\phi_H(n)=ex(n,H)+o(n^2) by Pikhurko and Sousa [J. Combin. Theory Ser. B 97 (2007), 1041-1055]. In addition it extends a result of \\\"Ozkahya and Person [J. Combin. Theory"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.2571","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"}