{"paper":{"title":"New bounds for locally irregular chromatic index of bipartite and subcubic graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Borut Lu\\v{z}ar, Jakub Przyby{\\l}o, Roman Sot\\'ak","submitted_at":"2016-11-07T23:34:05Z","abstract_excerpt":"A graph is \\textit{locally irregular} if the neighbors of every vertex $v$ have degrees distinct from the degree of $v$. \\textit{locally irregular edge-coloring} of a graph $G$ is an (improper) edge-coloring such that the graph induced on the edges of any color class is locally irregular. It is conjectured that $3$ colors suffice for a locally irregular edge-coloring. Recently, Bensmail et al. (Bensmail, Merker, Thomassen: Decomposing graphs into a constant number of locally irregular subgraphs, {\\em European J. Combin.}, 60:124--134, 2017) settled the first constant upper bound for the proble"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.02341","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"}