{"paper":{"title":"$(r)$-Pancyclic, $(r)$-Bipancyclic and Oddly $(r)$-Bipancyclic Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Abdollah Khodkar, Lisa Mueller, Oliver Sawin, WonHyuk Choi","submitted_at":"2015-10-11T13:41:47Z","abstract_excerpt":"A graph with $v$ vertices is $(r)$-pancyclic if it contains precisely $r$ cycles of every length from 3 to $v$. A bipartite graph with even number of vertices $v$ is said to be $(r)$-bipancyclic if it contains precisely $r$ cycles of each even length from 4 to $v$. A bipartite graph with odd number of vertices $v$ and minimum degree at least 2 is said to be oddly $(r)$-bipancyclic if it contains precisely $r$ cycles of each even length from 4 to $v-1$. In this paper, using computer search, we classify all $(r)$-pancyclic and $(r)$-bipancyclic graphs with $v$ vertices and at most $v+5$ edges. W"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.03052","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"}