Chromatic-index conjecture for signed complete graphs of even order

Let $K_n$ be the complete graph on $n$ vertices, let $\sigma$ be a signature on $K_n$, and let $\chi ' (K_n, \sigma)$ denote its signed chromatic index. Chromatic-index conjecture. If $n \geq 8$ is even, then

$$\chi ' (K_n, \sigma) = n-1.$$

The paper establishes the analogous signature-independent value for even orders $n=4$ and $n=6$; the asserted formula for all even $n\geq 8$ remains open based on the supplied text.