Minor-equivalence for infinite graphs Original Research Article

Two graphs are minor-equivalent if each is isomorphic to a minor of the other. In this paper, we give structural characterizations of the minor equivalence classes of the infinite full grid GZ × Z and of the infinite half-grid GZ × N. A corollary of these results states that every minor of GZ × Z that has a minor isomorphic to GZ × N is minor-equivalent to one of GZ × Z or GZ × N.