{"paper":{"title":"Domination versus edge domination","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Dieter Rautenbach, Elena Mohr, Julien Baste, Maximilian F\\\"urst, Michael A. Henning","submitted_at":"2019-06-25T09:47:23Z","abstract_excerpt":"We propose the conjecture that the domination number $\\gamma(G)$ of a $\\Delta$-regular graph $G$ with $\\Delta\\geq 1$ is always at most its edge domination number $\\gamma_e(G)$, which coincides with the domination number of its line graph. We prove that $\\gamma(G)\\leq \\left(1+\\frac{2(\\Delta-1)}{\\Delta 2^{\\Delta}}\\right)\\gamma_e(G)$ for general $\\Delta\\geq 1$, and $\\gamma(G)\\leq \\left(\\frac{7}{6}-\\frac{1}{204}\\right)\\gamma_e(G)$ for $\\Delta=3$. Furthermore, we verify our conjecture for cubic claw-free graphs."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.10420","kind":"arxiv","version":2},"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"}