Fragments and automorphisms of infinite graphs (Q798669)

The authors investigate the structure of infinite graphs \(\Gamma\) with \(\kappa_{\infty}(\Gamma)<\infty\) i.e. which can be separated into two or more infinite components by the removal of a finite number of vertices. The infinite components arising in this way are called fragments. A class of ''path-like'' graphs called strips are introduced. It is shown that if \(\Gamma\) is a vertex transitive graph and \(\kappa_{\infty}(\Gamma)<\infty\) then either \(\Gamma\) contains infinitely many pairwise disjoint fragments, or it is strip. The second half of the paper is devoted to a detailed study of strips and their automorphism groups.