On the Chromatic Number of the Products of Hypergraphs

This paper discusses the chromatic number of the products of \(n+1\) -chromatic hypergraphs. The following two results are proved:
Suppose \(G\) and \(H\) are \(n+ 1\) -chromatic hypergraphs such that each of \(G\) and \(H\) contains a complete sub-hypergraph of order n and each of \(G\)    and \(H\) contains a vertex critical \(n + 1\)-chromatic sub-hypergraph which has non-empty intersection with the corresponding complete sub-hypergraph of order \(n\). Then the product \(G \times H\)is of chromatic number \(n + 1\).
Suppose \(G\) is an \(n+ 1\)-chromatic hypergraph such that each vertex of \(G\) is contained in a complete sub-hypergraph of order n. Then for any \(n + 1\)-chromatic hypergraph \(H\), \(G \times H \) is an \(n + 1\)-chromatic hypergraph.