Uniform Šoltés' hypergraphs first occur at order 10, exist for every order n >= 10 and most uniformities k >= 4, a non-regular 9-uniform example exists, and infinitely many weighted Šoltés' graphs exist.
uniform šoltés’ hypergraphs and šoltés’ weighted graphs
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Uniform \v{S}olt\'es' hypergraphs and \v{S}olt\'es' weighted graphs
Uniform Šoltés' hypergraphs first occur at order 10, exist for every order n >= 10 and most uniformities k >= 4, a non-regular 9-uniform example exists, and infinitely many weighted Šoltés' graphs exist.