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A counter-example to Voloshin's hypergraph co-perfectness conjecture

The upper chromatic number χ(H) of a hypergraph H is the maximum number of colors in a coloring avoiding a polychromatic edge. The stability number α(H) of a hypergraph H is the cardinality of the largest set of vertices of H which does not contain an edge. A hypergraph is k-uniform if the sizes of all its edges are k. A hypergraph H is co-perfect if χ(H ′) = α(H ′) for each induced subhypergraph H ′ of H. Voloshin conjectured that an r-uniform hypergraph H (r ≥ 3) is co-perfect if and only if it contains neither of two special r-uniform hypergraphs (a so-called monostar and a complete circular r-uniform hypergraph on 2r − 1 vertices) as an induced subhypergraph. We disprove this conjecture for all r.