# Monotone paths on polytopes

@article{Athanasiadis2000MonotonePO, title={Monotone paths on polytopes}, author={Christos A. Athanasiadis and Paul H. Edelman and Victor Reiner}, journal={Mathematische Zeitschrift}, year={2000}, volume={235}, pages={315-334} }

Abstract. We investigate the vertex-connectivity of the graph of f-monotone paths on a d-polytopeP with respect to a generic functionalf. The third author has conjectured that this graph is always (d
$-1$)-connected. We resolve this conjecture positively for simple polytopes and show that the graph is 2-connected for any d-polytope with
$d \geq 3$. However, we disprove the conjecture in general by exhibiting counterexamples for each
$d \geq 4$ in which the graph has a vertex of degree two.We…

## 17 Citations

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