{"paper":{"title":"Scattered packings of cycles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","math.CO"],"primary_cat":"cs.DM","authors_text":"Aistis Atminas, Jean-Florent Raymond, Marcin Kami\\'nski","submitted_at":"2014-09-09T13:34:53Z","abstract_excerpt":"We consider the problem Scattered Cycles which, given a graph $G$ and two positive integers $r$ and $\\ell$, asks whether $G$ contains a collection of $r$ cycles that are pairwise at distance at least $\\ell$. This problem generalizes the problem Disjoint Cycles which corresponds to the case $\\ell = 1$. We prove that when parameterized by $r$, $\\ell$, and the maximum degree $\\Delta$, the problem Scattered Cycles admits a kernel on $24 \\ell^2 \\Delta^\\ell r \\log(8 \\ell^2 \\Delta^\\ell r)$ vertices. We also provide a $(16 \\ell^2 \\Delta^\\ell)$-kernel for the case $r=2$ and a $(148 \\Delta r \\log r)$-ke"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.2733","kind":"arxiv","version":4},"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"}