The end structure of a graph: Recent results and open problems (Q1198656)

This is a well-written survey about the recent development in the area of ends of infinite graphs. The author introduces the reader to the topic starting with the founding results and problems of Halin (1964), mentioning previous independent but related group-theoretical investigations of Hopf (1943) and Freudenthal (1944). The five sections: 1. Introduction. 2. End-faithful spanning trees, 3. One-ended graphs, 4. Endings and tree-decompositions, and 5. Topological aspects, present leading questions, important results (some provided with a proof), desription of methods and comments of an expert in the field. Reading of this paper will be useful to anyone interested to know more about this interesting part of the theory of infinite graphs.