Cycle-separating cut conjecture for cages

A $(k,g)$-cage is a smallest $k$-regular graph of girth $g$. A cycle-separating edge-cut is an edge-cut whose removal yields at least two components containing a cycle; a $g$-cycle is a cycle of length $g$.

Cycle-separating cut conjecture. For each $(k,g)$-cage $G$, every cycle-separating edge-cut of size $(k-2)g$ in $G$ separates a $g$-cycle.

This is presented as a strengthening of the conjectured maximal cyclic edge-connectivity of cages. Its resolution is not indicated in the source.