The classical Moore bound asserts that the girth of a graph on n vertices with minimal degree k is at least 2 log(n)/log(k-1). We extend Moore's bound to higher dimensional simplicial complexes, and use the Ramanujan Complexes of Lubotzky, Samuels and Vishne to show that the bound is essentially optimal.
Joint work with Alex Lubotzky.
Copyright. All Rights Reserved.