Kempe-equivalence characterization of perfectly contractile graphs

Let $G$ be a perfect graph. A replication graph $H$ of an induced subgraph of $G$ is obtained by replacing vertices of that induced subgraph by replicated vertices as defined in the paper. A $k$-coloring is a proper coloring using $k$ colors, and two $k$-colorings are Kempe equivalent if one can be obtained from the other by Kempe changes. The chromatic number of $H$ is denoted by $4\chi(H)4$.

Kempe-equivalence conjecture. The graph $G$ is perfectly contractile if and only if, for every replication graph $H$ of an arbitrary induced subgraph of $G$ and every $k \geq \chi(H)$, all $k$-colorings of $H$ are Kempe equivalent.

This would characterize perfectly contractile perfect graphs through the behavior of colorings of their replication graphs. The conjecture is presented as a new characterization, and the source gives no evidence that it has been resolved.