{"paper":{"title":"Weighted Efficient Domination for $(P_5+kP_2)$-Free Graphs in Polynomial Time","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Andreas Brandstadt, Vassilis Giakoumakis","submitted_at":"2014-07-17T08:11:57Z","abstract_excerpt":"Let $G$ be a finite undirected graph. A vertex {\\em dominates} itself and all its neighbors in $G$. A vertex set $D$ is an {\\em efficient dominating set} (\\emph{e.d.}\\ for short) of $G$ if every vertex of $G$ is dominated by exactly one vertex of $D$. The \\emph{Efficient Domination} (ED) problem, which asks for the existence of an e.d.\\ in $G$, is known to be \\NP-complete even for very restricted graph classes such as for claw-free graphs, for chordal graphs and for $2P_3$-free graphs (and thus, for $P_7$-free graphs). We call a graph $F$ a {\\em linear forest} if $F$ is cycle- and claw-free, i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.4593","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"}