Planar Strips and an End Concept for Digraphs

This thesis is divided into two parts. In the first part, an end concept for directed graphs is introduced and examined. For two one-way infinite directed paths Q and Q 0 of a digraph D define: a) Q Q 0 if there are infinitely many pairwise disjoint directed paths from Q to Q 0 ; b) Q ¸ Q 0 if Q Q 0 and Q 0 Q. The relation is a quasiorder, and hence ¸ is an equivalence relation (whose classes are called ends). Furthermore, induces a partial order on the set of ends of a digraph. A necessary and some sufficient condition(s) are presented for an abstract order to be representable by the end order of a digraph. Furthermore, there are several results concerning endfaithful super- and subdigraphs, translations of digraphs and ends of vertex-transitive digraphs. The main results of the first part are: 1) Every countable digraph with an initial vertex and no pair of -comparable w-ends contains an w-endfaithful, spanning arborescence. 2) Let D be an infinite, connected, ver..