{"paper":{"title":"A stronger bound for the strong chromatic index","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.PR"],"primary_cat":"math.CO","authors_text":"Felix Joos, Henning Bruhn","submitted_at":"2015-04-10T08:23:31Z","abstract_excerpt":"We prove $\\chi_s'(G)\\leq 1.93 \\Delta(G)^2$ for graphs of sufficiently large maximum degree where $\\chi_s'(G)$ is the strong chromatic index of $G$. This improves an old bound of Molloy and Reed. As a by-product, we present a Talagrand-type inequality where it is allowed to exclude unlikely bad outcomes that would otherwise render the inequality unusable."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.02583","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"}