On τ-tilting graphs for quasi-silted algebras

We prove that the $\tau$-tilting graph of any quasi-silted algebra is connected and has the reachable-in-face property. Our approach utilizes $\tau$-reduction and wall and chamber structures. In particular, we observe a sufficient condition on the wall and chamber structure under which the connectivity of $\tau$-tilting graphs is preserved under taking quotients of algebras. As an immediate consequence, the connectivity of $\tau$-tilting graphs is also established for several new classes of algebras.