{"paper":{"title":"Improved upper bounds on the domination number of graphs with minimum degree at least five","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Csilla Bujt\\'as, Sandi Klav\\v{z}ar","submitted_at":"2014-10-16T08:40:07Z","abstract_excerpt":"An algorithmic upper bound on the domination number $\\gamma$ of graphs in terms of the order $n$ and the minimum degree $\\delta$ is proved. It is demonstrated that the bound improves best previous bounds for any $5\\le \\delta \\le 50$. In particular, for $\\delta=5$, Xing et al.\\ proved in 2006 that $\\gamma \\le 5n/14 < 0.3572 n$. This bound is improved to $0.3440 n$. For $\\delta=6$, Clark et al.\\ in 1998 established $\\gamma <0.3377 n$, while Bir\\'o et al. recently improved it to $\\gamma <0.3340 n$. Here the bound is further improved to $\\gamma < 0.3159 n$. For $\\delta=7$, the best earlier bound $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.4334","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"}