{"paper":{"title":"$d$-Regular graphs of acyclic chromatic index at least $d+2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"L. Sunil Chandran, Manoj Kummini, Manu Basavaraju","submitted_at":"2008-04-29T19:18:52Z","abstract_excerpt":"An $acyclic$ edge coloring of a graph is a proper edge coloring such that there are no bichromatic cycles. The \\emph{acyclic chromatic index} of a graph is the minimum number k such that there is an acyclic edge coloring using k colors and is denoted by $a'(G)$. It was conjectured by Alon, Sudakov and Zaks\n  (and earlier by Fiamcik) that $a'(G)\\le \\Delta+2$, where $\\Delta =\\Delta(G)$ denotes the maximum degree of the graph. Alon et.al also raised the question whether the complete graphs of even order are the only regular graphs which require $\\Delta+2$ colors to be acyclically edge colored. In"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0804.4681","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"}