The Linear Chromatic Number of Sperner Families

Abstract

Let S be a set with m elements and S a complete Sperner family on S, i.e. a Sperner family such that every x ∈ S is contained in some member of S. The linear chromatic number of S, defined by Civan, is the smallest integer n with the property that there exists a function f : S → {1, . . . , n} such that if f(x) = f(y), then every set in S which contains x… (More)

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