{"paper":{"title":"An Efficient Algorithm for Mixed Domination on Generalized Series-Parallel Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.DM","authors_text":"A. Shakiba, M. J. Dinneen, M. Rajaati, M. R. Hooshmandasl, P. Sharifani","submitted_at":"2017-08-01T10:49:30Z","abstract_excerpt":"A mixed dominating set $S$ of a graph $G=(V,E)$ is a subset $ S \\subseteq V \\cup E$ such that each element $v\\in (V \\cup E) \\setminus S$ is adjacent or incident to at least one element in $S$. The mixed domination number $\\gamma_m(G)$ of a graph $G$ is the minimum cardinality among all mixed dominating sets in $G$. The problem of finding $\\gamma_{m}(G)$ is know to be NP-complete. In this paper, we present an explicit polynomial-time algorithm to construct a mixed dominating set of size $\\gamma_{m}(G)$ by a parse tree when $G$ is a generalized series-parallel graph."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.00240","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"}