Reduced form conjecture for shortest separating non-contractible cycles

A separating non-contractible cycle (SNCC) is a cycle in a triangulation that is separating and non-contractible. Let $t$ be a triangulation and let $C$ be an SNCC of $t$ of shortest length. Shortest SNCC reduction conjecture. It is impossible to write

$$C=\gamma^2C',$$

where $\gamma$ is a simple cycle.

This is a deterministic conjecture about the structure of a shortest separating non-contractible cycle. The paper presents it as a further open question at the end of its discussion of conjectures.