{"paper":{"title":"Queue Layouts of Graphs with Bounded Degree and Bounded Genus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"David R. Wood, Pat Morin, Vida Dujmovi\\'c","submitted_at":"2019-01-17T02:49:30Z","abstract_excerpt":"Motivated by the question of whether planar graphs have bounded queue-number, we prove that planar graphs with maximum degree $\\Delta$ have queue-number $O(\\Delta^{2})$, which improves upon the best previous bound of $O(\\Delta^6)$. More generally, we prove that graphs with bounded degree and bounded Euler genus have bounded queue-number. In particular graphs with Euler genus $g$ and maximum degree $\\Delta$ have queue-number $O(g+\\Delta^{2})$. As a byproduct we prove that if planar graphs have bounded queue-number, then graphs of Euler genus $g$ have queue-number $O(g)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.05594","kind":"arxiv","version":2},"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"}