{"paper":{"title":"Bounds on the 2-domination number","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Csilla Bujt\\'as, Szil\\'ard Jask\\'o","submitted_at":"2016-12-25T22:13:06Z","abstract_excerpt":"In a graph $G$, a set $D\\subseteq V(G)$ is called 2-dominating set if each vertex not in $D$ has at least two neighbors in $D$. The 2-domination number $\\gamma_2(G)$ is the minimum cardinality of such a set $D$. We give a method for the construction of 2-dominating sets, which also yields upper bounds on the 2-domination number in terms of the number of vertices, if the minimum degree $\\delta(G)$ is fixed. These improve the best earlier bounds for any $6 \\le \\delta(G) \\le 21$. In particular, we prove that $\\gamma_2(G)$ is strictly smaller than $n/2$, if $\\delta(G) \\ge 6$. Our proof technique u"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.08301","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"}