87 citations · 193 across the 17 of their papers we have counts for
5 papers · 1 filter
Simplicial spanning trees in random Steiner complexes
Ron Rosenthal, Lior Tenenbaum
A spanning tree in a graph is a sub-graph of with the same vertex set as which is a tree. In 1981, McKay proved an asymptotic result regarding the number of spannin…
On groups and simplicial complexes
Alexander Lubotzky, Zur Luria, Ron Rosenthal
The theory of -regular graphs is closely related to group theory. Every -regular, bipartite graph is a Schreier graph with respect to some group , a set of generators …
Random Steiner systems and bounded degree coboundary expanders of every dimension
Alexander Lubotzky, Zur Luria, Ron Rosenthal
We introduce a new model of random -dimensional simplicial complexes, for , whose -cells have bounded degrees. We show that with high probability, complexes samp…
Simplicial complexes: spectrum, homology and random walks
Ori Parzanchevski, Ron Rosenthal
Random walks on a graph reflect many of its topological and spectral properties, such as connectedness, bipartiteness and spectral gap magnitude. In the first part of this paper we…
Isoperimetric Inequalities in Simplicial Complexes
Ori Parzanchevski, Ron Rosenthal, Ran J. Tessler
In graph theory there are intimate connections between the expansion properties of a graph and the spectrum of its Laplacian. In this paper we define a notion of combinatorial expa…