Ends and tangles, stars and combs, minors and the Farey graph

Abstract

"It has been reported that Dénes König, the author of the classic Theorie der endlichen und unendlichen Graphen (Leipzig, 1936), expressed a special liking for infinite graphs, which certainly receive substantial attention in his book. Nevertheless, the majority of combinatorialists seem to have concentrated on finite combinatorics, to the extent that it has almost seemed an eccentricity to think that graphs and other combinatorial structures can be either finite or infinite. However, there seems to be no logical reason why combinatorial structures should usually' be finite, and indeed this would preclude many fascinating avenues of exploration." (C.St.J.A. Nash-Williams).

In this dissertation we will explore four exciting branches of structural infinite graph theory.