{"paper":{"title":"Generation of cubic graphs and snarks with large girth","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Gunnar Brinkmann, Jan Goedgebeur","submitted_at":"2015-12-18T13:31:18Z","abstract_excerpt":"We describe two new algorithms for the generation of all non-isomorphic cubic graphs with girth at least $k\\ge 5$ which are very efficient for $5\\le k \\le 7$ and show how these algorithms can be efficiently restricted to generate snarks with girth at least $k$.\n  Our implementation of these algorithms is more than 30, respectively 40 times faster than the previously fastest generator for cubic graphs with girth at least 6 and 7, respectively.\n  Using these generators we have also generated all non-isomorphic snarks with girth at least 6 up to 38 vertices and show that there are no snarks with "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.05944","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"}