{"paper":{"title":"Berge-Fulkerson coloring for infinite families of snarks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Rong-Xia Hao, Ting Zheng","submitted_at":"2017-08-23T04:22:46Z","abstract_excerpt":"It is conjectured by Berge and Fulkerson that every bridgeless cubic graph has six perfect matchings such that each edge is contained in exactly two of them. H$\\ddot{a}$gglund constructed two graphs Blowup$(K_4, C)$ and Blowup$(Prism, C_4)$. Based on these two graphs, Chen constructed infinite families of bridgeless cubic graphs $M_{0,1,2, \\ldots,k-2, k-1}$ which is obtained from cyclically 4-edge-connected and having a Fulkerson-cover cubic graphs $G_0,G_1,\\ldots, G_{k-1}$ by recursive process. If each $G_i$ for $1\\leq i\\leq k-1$ is a cyclically 4-edge-connected snarks with excessive index at"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.07122","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"}