Discrete Mathematics & Theoretical Computer Science, Vol 13, No 3 (2011)

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On the Book Thickness of k-Trees

David Wood, Vida Dujmović

Abstract


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.

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