{"paper":{"title":"The list chromatic index of simple graphs whose odd cycles intersect in at most one edge","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Gregory J. Puleo, Jessica McDonald","submitted_at":"2015-07-21T18:14:05Z","abstract_excerpt":"We study the class of simple graphs $\\mathcal{G}^*$ for which every pair of distinct odd cycles intersect in at most one edge. We give a structural characterization of the graphs in $\\mathcal{G}^*$ and prove that every $G \\in \\mathcal{G}^*$ satisfies the list-edge-coloring conjecture. When $\\Delta(G) \\geq 4$, we in fact prove a stronger result about kernel-perfect orientations in $L(G)$ which implies that $G$ is $(m\\Delta(G):m)$-edge-choosable and $\\Delta(G)$-edge-paintable for every $m \\geq 1$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.05933","kind":"arxiv","version":6},"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"}