This question is two-fold, and is mainly reference-oriented:Is there somewhere where the main intuitions for proving graph minor theorem are given, without going too much into the details? I know the proof is long and difficult, but surely there must be key ideas that can be communicated in an easier way.Are there other relations on graphs that can be shown to be well quasi-orders, maybe in a simpler way than for the minor relation? (obviously I am not interested in trivial results here, like comparing sizes). Directed graphs are also in the scope of the question.
Understanding graph minor theorem
reference request;graph theory;graph minor
The following book covers some material related to the proof of the graph minor theorem (Chapter 12). Reinhard Diestel: Graph Theory, 4th edition, Graduate Texts in Mathematics 173.The author states: [...] we have to be modest: of the actual proof of the minor theorem, this chapter will convey only a very rough impression. However, as with most truly fundamental results, the proof has sparked off the development of methods of quite independent interest and potential. An electronic version of the book can be viewed online. http://diestel-graph-theory.com/