On the book thickness of k-trees
Every k-tree has book thickness at most k + 1, and this bound is best possible for all k ≥ 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 ≥ 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.
|Keywords||Book embedding, Book thickness, Graph, Pagenumber, Stacknumber, Tree decomposition, Treewidth|
|Journal||Discrete Mathematics and Theoretical Computer Science|
Dujmović, V, & Wood, D. (2011). On the book thickness of k-trees. Discrete Mathematics and Theoretical Computer Science, 13(3), 39–44.