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We prove a linear upper bound on the function      n ( r ) = min { | H | : H n(r) = {\text {min}}\{ \left | {\mathcal {H}} \right |:\mathcal {H}       an      r r      -uniform, intersecting hypergraph with      τ  ( H ) = r } \tau (\mathcal {H}) = r\}      , thus settling a longstanding problem of Erdös and Lovász.

On a problem of Erdős and Lovász. II. 𝑛(𝑟)=𝑂(𝑟)