{"paper":{"title":"A Gap in the 42-Queue Layout Algorithm for Planar Graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Sergey Pupyrev","submitted_at":"2026-08-06T01:22:53Z","abstract_excerpt":"A queue layout of a graph consists of a linear order of the vertices and a partition of the edges into queues so that no two edges in a single queue are nested. The minimum number of queues needed in a queue layout of a graph is called its queue number. The planar product structure theorem states that every planar graph is a subgraph of the strong product of a graph of simple treewidth at most $3$, a clique $K_3$, and a path. Such a strong product admits a queue layout with $49$ queues (Wood, 2005), which implies that the queue number of planar graphs is at most $49$.\n  Recently, Bekos, Gronem"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.05508","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2608.05508/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}