{"paper":{"title":"On Gallai's and Haj\\'os' Conjectures for graphs with treewidth at most 3","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"F\\'abio Botler, Maycon Sambinelli, Orlando Lee, Rafael S. Coelho","submitted_at":"2017-06-14T07:03:06Z","abstract_excerpt":"A path (resp. cycle) decomposition of a graph $G$ is a set of edge-disjoint paths (resp. cycles) of $G$ that covers the edge set of $G$. Gallai (1966) conjectured that every graph on $n$ vertices admits a path decomposition of size at most $\\lfloor (n+1)/2\\rfloor$, and Haj\\'os (1968) conjectured that every Eulerian graph on $n$ vertices admits a cycle decomposition of size at most $\\lfloor (n-1)/2\\rfloor$. Gallai's Conjecture was verified for many classes of graphs. In particular, Lov\\'asz (1968) verified this conjecture for graphs with at most one vertex of even degree, and Pyber (1996) verif"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.04334","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"}