Not all simplicial polytopes are weakly vertex-decomposable

Details Not all simplicial polytopes are weakly vertex-decomposable Not all simplicial polytopes are weakly vertex-decomposable

2012-03-08

arxiv.org/abs/1203.1676v1

Mathematics

Combinatorics

Scientific paper

In 1980 Provan and Billera defined the notion of weak $k$-decomposability for pure simplicial complexes. They showed the diameter of a weakly $k$-decomposable simplicial complex $\Delta$ is bounded above by a polynomial function of the number of $k$-faces in $\Delta$ and its dimension. For weakly 0-decomposable complexes, this bound is linear in the number of vertices and the dimension. In this paper we exhibit the first examples of non-weakly 0-decomposable simplicial polytopes.

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