{"paper":{"title":"On the Edit Distance of Powers of Cycles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Chelsea Peck, Ryan R. Martin, Zhanar Berikkyzy","submitted_at":"2015-09-24T17:03:27Z","abstract_excerpt":"The edit distance between two graphs on the same labeled vertex set is defined to be the size of the symmetric difference of the edge sets. The edit distance function of a hereditary property $\\mathcal{H}$ is a function of $p\\in [0,1]$ that measures, in the limit, the maximum normalized edit distance between a graph of density $p$ and $\\mathcal{H}$.\n  In this paper, we address the edit distance function for $\\mbox{Forb}(H)$, where $H=C_h^t$, the $t^{\\rm th}$ power of the cycle of length $h$. For $h\\geq 2t(t+1)+1$ and $h$ not divisible by $t+1$, we determine the function for all values of $p$. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.07438","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"}