On the book thickness of $k$-trees

Details On the book thickness of $k$-trees On the book thickness of $k$-trees

2009-11-21

arxiv.org/abs/0911.4162v1

Mathematics

Combinatorics

Scientific paper

Every $k$-tree has book thickness at most $k+1$, and this bound is best possible for all $k\geq3$. Vandenbussche et al. (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 $k\geq 4$, 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. (2009)

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