Matching arc complexes: connectedness and hyperbolicity
Javier Aramayona, Rodrigo de Pool, Alejandro Fern\'andez
TL;DR
This paper establishes conditions on finite graphs that ensure their associated matching arc complexes are both connected and hyperbolic, advancing understanding in geometric group theory and topological combinatorics.
Contribution
It provides new criteria linking graph properties to the topological and geometric features of matching arc complexes, answering a question posed by Zaremsky.
Findings
Matching arc complexes are connected under certain graph conditions.
Matching arc complexes are hyperbolic given specific criteria.
The paper answers Zaremsky's question on these complexes.
Abstract
Addressing a question of Zaremsky, we give conditions on a finite simplicial graph which guarantee that the associated matching arc complex is connected and hyperbolic.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.