Welcome to Structural Graph Theory! The purpose of this course is to provide an introduction to some of the central results and methods of structural graph theory. Our main point of emphasis will be on graph minor theory and the concepts devised in Robertson and Seymour's intricate proof of the Graph Minor Theorem: in every infinite set of graphs there are two graphs such that one is a minor of the other. This implies, as we shall see, that every minor-closed graph property can be described by a list of finitely many forbidden minors, massively generalizing the Kuratowski-Wagner theorem for planar graphs. Our second point of emphasis, if time permits, will be on Hadwiger's conjecture: that every graph with chromatic number at least r contains a clique minor on r vertices.
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