{"paper":{"title":"Linear rank-width of distance-hereditary graphs I. A polynomial-time algorithm","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","cs.DS"],"primary_cat":"math.CO","authors_text":"Isolde Adler, Mamadou Moustapha Kant\\'e, O-joung Kwon","submitted_at":"2014-03-05T11:27:38Z","abstract_excerpt":"Linear rank-width is a linearized variation of rank-width, and it is deeply related to matroid path-width. In this paper, we show that the linear rank-width of every $n$-vertex distance-hereditary graph, equivalently a graph of rank-width at most $1$, can be computed in time $\\mathcal{O}(n^2\\cdot \\log_2 n)$, and a linear layout witnessing the linear rank-width can be computed with the same time complexity. As a corollary, we show that the path-width of every $n$-element matroid of branch-width at most $2$ can be computed in time $\\mathcal{O}(n^2\\cdot \\log_2 n)$, provided that the matroid is gi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.1081","kind":"arxiv","version":3},"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"}