\(C\)-Perfect \(K\)-Uniform Hypergraphs

Abstract

In this paper, the concept of clique number of uniform hypergraph is defined and its relationship with circular chromatic number and clique number is studied. For every positive integer \(k, p\) and \(q\), \(2q \leq p\) we construct a \(k\)-uniform hypergraph with small clique number whose circular chromatic number is equal to \(\frac{p}{q}\). We define the concept and study the properties of \(c\)-perfect \(k\)-uniform hypergraphs.