Shellability of complexes of directed trees
Abstract
The question of shellability of complexes of directed trees was asked by R. Stanley. D. Kozlov showed that the existence of a complete source in a directed graph provides a shelling of its complex of directed trees. We will show that this property gives a shelling that is straightforward in some sense. Among the simplicial polytopes, only the crosspolytopes allow such a shelling. Furthermore, we show that the complex of directed trees of a complete double directed graph is a union of suitable spheres. We also investigate shellability of the maximal pure skeleton of a complex of directed trees. Also, we prove that is vertex-decomposable. For these complexes we describe the set of generating facets.
Keywords
Cite
@article{arxiv.1109.4475,
title = {Shellability of complexes of directed trees},
author = {Duško Jojić},
journal= {arXiv preprint arXiv:1109.4475},
year = {2012}
}
Comments
This is a new version in which Section 3 about complexes $\mathcal{C}_n^k$ is removed. There are some troubles in the proof of Theorem 14. We add a new section about the complexes of directed trees of a directed graph which is essentially a tree