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The Princeton Companion to Mathematics by Imre Leader, June Barrow-Green, Timothy Gowers

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V.32 The Robertson-Seymour Theorem

Bruce Reed

A graph G is a mathematical structure that consists of a set V(G) of vertices and a set E(G) of edges, where each edge links a pair of vertices. Graphs can be used to represent many different networks in an abstract way. For example, the vertices might represent cities, and the edges might represent highways linking the cities; similarly, we could use a graph to represent which islands of an archipelago are linked by bridges, or to represent the wires of a telephone network. Among graphs there are certain families of “nice” graphs. One such family is the family of cycles: a k-cycle is a set of k vertices arranged around a circle with each point joined by an edge to the points immediately before ...

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