{"paper":{"title":"A Planar Linear Arboricity Conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Borut Luzar, Lukasz Kowalik, Marek Cygan","submitted_at":"2009-12-30T20:15:50Z","abstract_excerpt":"The linear arboricity la(G) of a graph G is the minimum number of linear forests that partition the edges of G. In 1984, Akiyama et al. stated the Linear Arboricity Conjecture (LAC), that the linear arboricity of any simple graph of maximum degree $\\Delta$ is either $\\lceil \\tfrac{\\Delta}{2} \\rceil$ or $\\lceil \\tfrac{\\Delta+1}{2} \\rceil$. In [J. L. Wu. On the linear arboricity of planar graphs. J. Graph Theory, 31:129-134, 1999] and [J. L. Wu and Y. W. Wu. The linear arboricity of planar graphs of maximum degree seven is four. J. Graph Theory, 58(3):210-220, 2008.] it was proven that LAC holds"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.5528","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"}