{"paper":{"title":"Degree conditions for the partition of a graph into triangles and quadrilaterals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Jian-Liang Wu, Jin Yan, Xin Zhang","submitted_at":"2010-12-29T12:15:22Z","abstract_excerpt":"For two positive integers $r$ and $s$ with $r\\geq 2s-2$, if $G$ is a graph of order $3r+4s$ such that $d(x)+d(y)\\geq 4r+4s$ for every $xy\\not\\in E(G)$, then $G$ independently contains $r$ triangles and $s$ quadrilaterals, which partially prove the El-Zahar's Conjecture."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.5920","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"}