{"paper":{"title":"Improved Domination--Packing Bounds in Claw-Free Cubic Graphs and Unit Disk Graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Juan Guti\\'errez, Kaustav Paul","submitted_at":"2026-06-28T04:58:55Z","abstract_excerpt":"Given a graph $G$, the domination number $\\gamma(G)$ is the minimum cardinality of a dominating set in $G$, and the packing number $\\rho(G)$ is the maximum cardinality of a set of vertices that are pairwise at distance at least $3$. The ratio between these parameters has been widely studied in several graph classes. It is known that $\\gamma(G) \\le 2\\rho(G)$ for claw-free subcubic graphs, up to finitely many exceptions, and that $\\gamma(G) \\le 32\\rho(G)$ for unit disk graphs. In this paper, we improve the latter bound by showing that $\\gamma(G) \\le 16\\rho(G)$ for a unit disk graph $G$. For the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.29199","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.29199/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}