On the chromaticity of sunflower hypergraphs SH(n, p, h)

A sunflower hypergraph SH(n, p, h) is an h-hypergraph of order n = h + (k − 1)p and size k (1 p h − 1 and h 3), where each edge (or a “petal”) consists of p distinct vertices and a common subset to all edges with h−p vertices. In this paper, it is shown that this hypergraph is h-chromatically unique (i.e., chromatically unique in the set of all h-hypergraphs) for every 1 p h − 2, but this is not true for p = h− 1 and k 3. Also SH(n, p, h) is not chromatically unique for every p, k 2. © 2006 Elsevier B.V. All rights reserved.