Exchange graphs of cluster algebras have the non-leaving-face property

TL;DR

This paper proves that exchange graphs of cluster algebras possess the non-leaving-face property, confirming a structural characteristic of these mathematical objects.

Contribution

The paper provides a formal proof that exchange graphs of cluster algebras have the non-leaving-face property, a previously conjectured structural feature.

Findings

Exchange graphs have the non-leaving-face property

The proof confirms a key structural aspect of cluster algebras

Supports further theoretical understanding of cluster algebra combinatorics

Abstract

The claim in the title is proved.