# Enumerative problems for arborescences and monotone paths on polytopes

@article{Athanasiadis2020EnumerativePF, title={Enumerative problems for arborescences and monotone paths on polytopes}, author={Christos A. Athanasiadis and Jes{\'u}s A. De Loera and Zhenyang Zhang}, journal={arXiv: Combinatorics}, year={2020} }

Every generic linear functional $f$ on a convex polytope $P$ orients the edges of the graph of $P$. In this directed graph one can define a notion of $f$-arborescence and $f$-monotone path on $P$. Additionally, a natural notion of adjacency between pairs of $f$-monotone paths gives us the so called flip graph of $f$-monotone paths. These concepts are of importance in geometric combinatorics and optimization.
We investigate the extreme values of the number of $f$-arborescences, the number of $f…

## 2 Citations

### Enumerative problems for arborescences and monotone paths on polytope graphs

- MathematicsJ. Graph Theory
- 2022

The number of f-arborescence and f-monotone paths, the number of vertices or facets of the graph of f, and the diameter of theGraph of f for polytopes P are bounds in terms of their dimension and number of vertex set.

### Graph of uv-paths in 2-connected graphs

- Mathematics
- 2021

For a 2-connected graph G and vertices u, v of G we define an abstract graph P(Guv) whose vertices are the paths joining u and v in G, where paths S and T are adjacent if T is obtained from S by…

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