Vida Dujmović ; David R. Wood - On the Book Thickness of k-Trees

dmtcs:550 - Discrete Mathematics & Theoretical Computer Science, October 17, 2011, Vol. 13 no. 3 - https://doi.org/10.46298/dmtcs.550
On the Book Thickness of k-Trees

Authors: Vida Dujmović ; David R. Wood

    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.


    Volume: Vol. 13 no. 3
    Section: Graph and Algorithms
    Published on: October 17, 2011
    Accepted on: June 9, 2015
    Submitted on: November 25, 2010
    Keywords: [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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