Geodesics and almost geodesic cycles in random regular graphs

Itai Benjamini, Carlos Hoppen, Eran Ofek, Pawel Pralat, Nicholas C. Wormald

Abstract: A geodesic in a graph G is a shortest path between two vertices of G. For a specific function e(n) of n, we define an almost geodesic cycle C in G to be a cycle in which for every two vertices u and ...