Author:
Biermann Jennifer,Van Tuyl Adam
Abstract
Given any finite simplicial complex $\Delta$, we show how to construct from a colouring $\chi$ of $\Delta$ a new simplicial complex $\Delta_{\chi}$ that is balanced and vertex decomposable. In addition, the $h$-vector of $\Delta_{\chi}$ is precisely the $f$-vector of $\Delta$. Our construction generalizes the "whiskering'' construction of Villarreal, and Cook and Nagel. We also reverse this construction to prove a special case of a conjecture of Cook and Nagel, and Constantinescu and Varbaro on the $h$-vectors of flag complexes.
Publisher
The Electronic Journal of Combinatorics
Subject
Computational Theory and Mathematics,Geometry and Topology,Theoretical Computer Science,Applied Mathematics,Discrete Mathematics and Combinatorics
Cited by
12 articles.
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