{"paper":{"title":"The probabilistic approach to limited packings in graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Andrei Gagarin, Vadim Zverovich","submitted_at":"2013-11-07T15:02:40Z","abstract_excerpt":"We consider (closed neighbourhood) packings and their generalization in graphs. A vertex set X in a graph G is a k-limited packing if for any vertex $v\\in V(G)$, $\\left|N[v] \\cap X\\right| \\le k$, where N[v] is the closed neighbourhood of v. The k-limited packing number $L_k(G)$ of a graph G is the largest size of a k-limited packing in G. Limited packing problems can be considered as secure facility location problems in networks.\n  In this paper, we develop a new probabilistic approach to limited packings in graphs, resulting in lower bounds for the k-limited packing number and a randomized al"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.1707","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"}