On the Book Thickness of k-Trees

Vida Dujmović (1) , David R. Wood (2)

1 School of Computer Science [Ottawa]
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.

Domaines: Mathématique discrète [cs.DM]

Vida Dujmović, David R. Wood. On the Book Thickness of k-Trees. Discrete Mathematics and Theoretical Computer Science, 2011, Vol. 13 no. 3 (3), pp.39--44. ⟨10.46298/dmtcs.550⟩. ⟨hal-00990475⟩