Darij Grinberg, Lukas Katthän, Joel Brewster Lewis
Published 2021-02-15Version 1
We study the homotopy type and other properties of two simplicial complexes arising from a directed graph $G = (V, E)$ with two chosen vertices $s$ and $t$: the *path-free complex*, consisting of all subsets $F \subseteq E$ that contain no path from $s$ to $t$, and the *path-missing complex*, its Alexander dual.
On the homotopy type of multipath complexes
On D.K. Biss' papers "The homotopy type of the matroid Grassmannian" and "Oriented matroids, complex manifolds, and a combinatorial model for BU"
Matching trees for simplicial complexes and homotopy type of devoid complexes of graphs
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