The four-colour theorem is likely one of the well-known difficulties of arithmetic, that annoyed generations of mathematicians from its delivery in 1852 to its answer (using gigantic the aid of digital desktops) in 1976. the theory asks no matter if 4 colors are enough to color all achievable maps, in the sort of approach that nations with a typical border are colored with various colors. The booklet discusses numerous makes an attempt to resolve this challenge, and a few of the math which constructed out of those makes an attempt. a lot of this arithmetic has built a lifetime of its personal, and types a desirable a part of the topic referred to now as graph conception. The booklet is designed to be self-contained, and develops all of the graph theoretical instruments wanted because it is going alongside. It contains all of the undemanding graph conception that are supposed to be integrated in an advent to the topic, prior to focusing on particular issues suitable to the four-colour challenge. half I covers uncomplicated graph conception, Euler's polyhedral formulation, and the 1st released fake facts of the four-colour theorem. half II levels commonly via similar subject matters, together with map-colouring on surfaces with holes, the well-known theorems of Kuratowski, Vizing, and Brooks, the conjectures of Hadwiger and Hajos, and masses extra along with. partially III we go back to the four-colour theorem, and examine intimately the tools which ultimately cracked the problem.
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