2 Department of Mathematics and Statistics [Melbourne]
Every k-tree has book thickness at most k + 1, and this bound is best possible for all k \textgreater= 3. Vandenbussche et al. [SIAM J. Discrete Math., 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 \textgreater= 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.
Funder: Natural Sciences and Engineering Research Council of Canada
Bibliographic References
1 Document citing this article
Sujoy Bhore;Robert Ganian;Fabrizio Montecchiani;Martin Nöllenburg, 2020, Parameterized Algorithms for Book Embedding Problems, Journal of Graph Algorithms and Applications, 24, 4, pp. 603-620, 10.7155/jgaa.00526, https://doi.org/10.7155/jgaa.00526.