2011/09/21 by Duško Jojić, Jojić, Duško
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #Commutative Algebra and Its Applications #FOS: Mathematics #Topological and Geometric Data Analysis #math.CO
paper · pdf · doi:10.48550/arxiv.1109.4475
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
openalex publication_date 2011/09/21 · arxiv created 2012/04/13 · arxiv updated 2012/04/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.