{"paper":{"title":"On the book thickness of $k$-trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"David R. Wood, Vida Dujmovi\\'c","submitted_at":"2009-11-21T05:39:48Z","abstract_excerpt":"Every $k$-tree has book thickness at most $k+1$, and this bound is best possible for all $k\\geq3$. Vandenbussche et al. (2009) proved that every $k$-tree that has a smooth degree-3 tree decomposition with width $k$ has book thickness at most $k$. We prove this result is best possible for $k\\geq 4$, by constructing a $k$-tree with book thickness $k+1$ that has a smooth degree-4 tree decomposition with width $k$. This solves an open problem of Vandenbussche et al. (2009)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.4162","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"}