{"paper":{"title":"On graph classes with constant domination-packing ratio","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Anna Gujgiczer, Marthe Bonamy, M\\'onika Csik\\'os, Yelena Yuditsky","submitted_at":"2025-03-07T16:40:09Z","abstract_excerpt":"The dominating number $\\gamma(G)$ of a graph $G$ is the minimum size of a vertex set whose closed neighborhood covers all the vertices of the graph. The packing number $\\rho(G)$ of $G$ is the maximum size of a vertex set whose closed neighborhoods are pairwise disjoint. In this paper we study graph classes ${\\cal G}$ such that $\\gamma(G)/\\rho(G)$ is bounded by a constant $c_{\\cal G}$ for each $G\\in {\\cal G}$. We propose an inductive proof technique to prove that if $\\cal G$ is the class of $2$-degenerate graphs, then there is such a constant bound $c_{\\cal G}$. We note that this is the first m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.05562","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/2503.05562/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"}