{"paper":{"title":"Decomposing graphs into a constant number of locally irregular subgraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Carsten Thomassen, Julien Bensmail, Martin Merker","submitted_at":"2016-04-01T13:30:13Z","abstract_excerpt":"A graph is locally irregular if no two adjacent vertices have the same degree. The irregular chromatic index $\\chi_{\\rm irr}'(G)$ of a graph $G$ is the smallest number of locally irregular subgraphs needed to edge-decompose $G$. Not all graphs have such a decomposition, but Baudon, Bensmail, Przyby{\\l}o, and Wo\\'zniak conjectured that if $G$ can be decomposed into locally irregular subgraphs, then $\\chi_{\\rm irr}'(G)\\leq 3$. In support of this conjecture, Przyby{\\l}o showed that $\\chi_{\\rm irr}'(G)\\leq 3$ holds whenever $G$ has minimum degree at least $10^{10}$.\n  Here we prove that every bipa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.00235","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"}