4 citations · 13 across the 4 of their papers we have counts for
4 papers
Expanders are order diameter non-hyperbolic
Anton Malyshev
We show that expander graphs must have Gromov-hyperbolicity at least proportional to their diameter, with a constant of proportionality depending only on the expansion constant and…
Lifts, derandomization, and diameters of Schreier graphs of Mealy automata
Anton Malyshev, Igor Pak
It is known that random 2-lifts of graphs give rise to expander graphs. We present a new conjectured derandomization of this construction based on certain Mealy automata. We verify…
Non-amenability of product replacement graphs
Anton Malyshev
We prove non-amenability of the product replacement graphs Γ_n(G) for uniformly non-amenable groups. We also prove it for Z-large groups, when n is sufficiently large. It follows t…
Growth in product replacement graphs
Anton Malyshev, Igor Pak
We prove the exponential growth of product replacement graphs for a large class of groups. Much of our effort is dedicated to the study of product replacement graphs of Grigorchuk…