{"paper":{"title":"Relating Domination, Exponential Domination, and Porous Exponential Domination","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Dieter Rautenbach, Michael A. Henning, Simon J\\\"ager","submitted_at":"2016-05-15T16:48:45Z","abstract_excerpt":"The domination number $\\gamma(G)$ of a graph $G$, its exponential domination number $\\gamma_e(G)$, and its porous exponential domination number $\\gamma_e^*(G)$ satisfy $\\gamma_e^*(G)\\leq \\gamma_e(G)\\leq \\gamma(G)$. We contribute results about the gaps in these inequalities as well as the graphs for which some of the inequalities hold with equality. Relaxing the natural integer linear program whose optimum value is $\\gamma_e^*(G)$, we are led to the definition of the fractional porous exponential domination number $\\gamma_{e,f}^*(G)$ of a graph $G$. For a subcubic tree $T$ of order $n$, we show"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.04575","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"}