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We show that the conjecture, if true, is also sharp for the smallest previously open value, namely $r=7$. For $r\\in\\{6,7\\}$, we find the minimal number $f(r)$ of edges in an intersecting $r$-partite hypergraph that has covering number at least $r-1$. 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Wanless, J\\'anos Bar\\'at, Ron Aharoni","submitted_at":"2014-09-16T23:51:14Z","abstract_excerpt":"A famous conjecture of Ryser is that in an $r$-partite hypergraph the covering number is at most $r-1$ times the matching number. If true, this is known to be sharp for $r$ for which there exists a projective plane of order $r-1$. We show that the conjecture, if true, is also sharp for the smallest previously open value, namely $r=7$. For $r\\in\\{6,7\\}$, we find the minimal number $f(r)$ of edges in an intersecting $r$-partite hypergraph that has covering number at least $r-1$. 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