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

A sunflower hypergraph SH(n,p,h)SH(n,p,h) is an h  -hypergraph of order n=h+(k-1)pn=h+(k-1)p and size k   (1⩽p⩽h-11⩽p⩽h-1 and h⩾3h⩾3), where each edge (or a “petal”) consists of p   distinct vertices and a common subset to all edges with h-ph-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-21⩽p⩽h-2, but this is not true for p=h-1p=h-1 and k⩾3k⩾3. Also SH(n,p,h)SH(n,p,h) is not chromatically unique for every p,k⩾2p,k⩾2.