eng
episciences.org
Discrete Mathematics & Theoretical Computer Science
1365-8050
2011-10-17
Vol. 13 no. 3
Graph and Algorithms
10.46298/dmtcs.550
550
journal article
On the Book Thickness of k-Trees
Vida Dujmović
David R. Wood
Graphs and Algorithms
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.
https://dmtcs.episciences.org/550/pdf
[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]