The algebraic Conforti–Cornuéjols conjecture on normality of the Rees algebra

Let $\cal C$ be a clutter, let $\tau({\cal C}')$ and $\nu({\cal C}')$ denote the minimum vertex-cover and maximum matching sizes of a minor $\cal C'$, and let $R[It]$ be the Rees algebra of the edge ideal $I$. Algebraic Conforti–Cornuéjols conjecture. If $\tau({\cal C}')=\nu({\cal C}')$ for all minors $\cal C'$ of $\cal C$, then $R[It]$ is normal. This is stated as an algebraic version of the packing-property conjecture and is presented as unresolved in the source.