In every sufficiently large structure which has been partitioned
there will always be some well-behaved structure in one of the
parts. This takes many forms. For example, colorings of the
integers by finitely many colors must have long monochromatic
arithmetic progressions (van der Waerden's theorem); and colorings
of the edges of large graphs must have monochromatic subgraphs of a
specified type (Ramsey's theorem). This book explores many of the
basic results and variations of this theory. Since the first
edition of this book there have been many advances in this field.
In the second edition the authors update the exposition to reflect
the current state of the art. They also include many pointers to
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