Colorability conjecture for cyclic pseudo-Loupekine graphs with parity conditions

Let $S$ be a Loupekine 5-pole, let $x\in\{\alpha,\beta\}$, and let $S_x(m;a,a,c)$ denote the associated cyclic pseudo-Loupekine graph. Assume that $m/\gcd(m,a)$ is even and $m/\gcd(m,c)$ is odd. Cyclic pseudo-Loupekine colorability conjecture. All such graphs $S_x(m;a,a,c)$ are 3-edge-colorable. This conjecture concerns a broad generalization of Loupekine's construction; the supplied text gives no resolution or partial proof.