General Edge-isoperimetric Inequalities, Part I: Information-theoretical Methods

Abstract In combinatorics we often meet two kinds of extremal problems. In one kind, optimal configurations consist of ‘objects’, which are somehow uniformly spread in the space under consideration; and in the other kind, optimal configurations consist of ‘objects’, which are somehow compressed. To the first kind belong packing, covering and coding problems, whereas diametric (especially of Erdos-Ko-Rado type), vertex- and edge-isoperimetric problems belong to the second kind.

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