Pairing conjecture for non-self-complementary transversal graphs

Let $m\geqslant 0$ and let $\mathbb{R}_{m,m}$ be the real representation of the Clifford algebra. A transversal graph is an induced complete subgraph on $2^m$ vertices, and its edges are coloured according to whether the corresponding basis-matrix pairs are amicable or anti-amicable. A graph is self-edge-colour complementary when it is unchanged by exchanging the two edge colours. Pairing conjecture for non-self-complementary transversal graphs. The transversal graphs that are not self-edge-colour complementary can be arranged into pairs such that each graph in a pair is edge-colour complementary to the other. This conjecture proposes a pairing of the non-self-complementary transversal graphs under colour exchange; the supplied source does not state a resolution.