We introduce and study swap cosystolic expansion, a new expansion property of simplicial complexes. We prove lower bounds for swap coboundary expansion of spherical buildings and use them to lower bound swap cosystolic expansion of the LSV Ramanujan complexes. Our motivation is the recent work (in a companion paper) showing ... more >>>

We consider the query complexity of testing whether a bounded-degree graph is expanding, regardless of whether or not it is connected.

Whereas prior work studied testing the property of being an expander (equiv., testing the set of expander graphs), here we study testing the set of graphs that consist of ... more >>>