| General edge-isoperimetric inequalities Part II. A local-global principle for lexicographical solutions | |||||||||||||||
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| Introduction The lexicographical order L on a sequence space X n = f0; 1; : : : ; ffg n , defined by x n ! L ! y n iff there exists a t such that x t ! y t and x s = y s for s ! t, is one of the most important and frequently encountered orders in combinatorial extremal theory. An early result in this area, Harper's solution of an edge--isoperimetric problem (EIP) in binary Hamming space ([13]) (generalized in [16] to nonbinary cases and rediscovered many times, e.g. [6], [9], [15]) says that first segments in L are optimal. There are two kinds of EIP. They can be represented as extremal problems in graph theory. Let G = (V; E) be | |||||||||||||||
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