{"paper":{"title":"Dominating Induced Matchings for P7-Free Graphs in Linear Time","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Andreas Brandstadt, Raffaele Mosca","submitted_at":"2011-06-14T18:09:20Z","abstract_excerpt":"Let $G$ be a finite undirected graph with edge set $E$. An edge set $E' \\subseteq E$ is an {\\em induced matching} in $G$ if the pairwise distance of the edges of $E'$ in $G$ is at least two; $E'$ is {\\em dominating} in $G$ if every edge $e \\in E \\setminus E'$ intersects some edge in $E'$. The \\emph{Dominating Induced Matching Problem} (\\emph{DIM}, for short) asks for the existence of an induced matching $E'$ which is also dominating in $G$; this problem is also known as the \\emph{Efficient Edge Domination} Problem.\n  The DIM problem is related to parallel resource allocation problems, encoding"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.2772","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"}