Finite common coverings of graphs

Abstract

It is easily shown that two finite graphs share a common (possibly infinite) cover if and only if they have the same degree refinement. Angluin and Gardiner (J. Combin. Theory Ser. B30 (1981), 184-187) show that any pair of regular graphs with identical valence share a common finite cover. More generally, they conjecture that any pair of graphs with the same degree refinement share a common finite cover. In this paper, their conjecture is verified and a method of constructing a finite common covering of any pair of graphs with the same degree refinement is defined. © 1982.