{"paper":{"title":"Layout of Graphs with Bounded Tree-Width","license":"","headline":"","cross_cats":["cs.CG"],"primary_cat":"cs.DM","authors_text":"David R. Wood, Pat Morin, Vida Dujmovic","submitted_at":"2004-06-16T15:29:07Z","abstract_excerpt":"A \\emph{queue layout} of a graph consists of a total order of the vertices, and a partition of the edges into \\emph{queues}, such that no two edges in the same queue are nested. The minimum number of queues in a queue layout of a graph is its \\emph{queue-number}. A \\emph{three-dimensional (straight-line grid) drawing} of a graph represents the vertices by points in $\\mathbb{Z}^3$ and the edges by non-crossing line-segments. This paper contributes three main results:\n  (1) It is proved that the minimum volume of a certain type of three-dimensional drawing of a graph $G$ is closely related to th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cs/0406024","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"}