{"paper":{"title":"A note on the edge partition of graphs containing either a light edge or an alternating 2-cycle","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Bei Niu, Xin Zhang","submitted_at":"2018-09-08T13:20:01Z","abstract_excerpt":"Let $\\mathcal{G}_{\\alpha}$ be a hereditary graph class (i.e, every subgraph of $G_{\\alpha}\\in \\mathcal{G}_{\\alpha}$ belongs to $\\mathcal{G}_{\\alpha}$) such that every graph $G_{\\alpha}$ in $\\mathcal{G}_{\\alpha}$ has minimum degree at most 1, or contains either an edge $uv$ such that $d_{G_{\\alpha}}(u)+d_{G_{\\alpha}}(v)\\leq \\alpha$ or a 2-alternating cycle. It is proved that every graph in $\\mathcal{G}_{\\alpha}$ ($\\alpha\\geq 5$) with maximum degree $\\Delta$ can be edge-partitioned into two forests $F_1$, $F_2$ and a subgraph $H$ such that $\\Delta(F_i)\\leq \\max\\{2,\\lceil\\frac{\\Delta-\\alpha+6}{2}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.02799","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"}