{"paper":{"title":"Induced 2-Regular Subgraphs in k-Chordal Cubic Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Christian L\\\"owenstein, Dieter Rautenbach, Felix Joos, Michael A. Henning","submitted_at":"2014-06-10T06:53:43Z","abstract_excerpt":"We show that a cubic graph $G$ of order $n$ has an induced $2$-regular subgraph of order at least a) $\\frac{n-2}{4-\\frac{4}{k}}$, if $G$ has no induced cycle of length more than $k$, b) $\\frac{5n+6}{8}$, if $G$ has no induced cycle of length more than $4$, and $n>6$, and c) $\\left(\\frac{1}{4}+\\epsilon\\right)n$, if the independence number of $G$ is at most $\\left(\\frac{3}{8}-\\epsilon\\right)n$. To show the second result we give a precise structural description of cubic $4$-chordal graphs."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.2438","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"}