Existence conjecture for edge-colour complements of 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 whose edges represent pairs of basis matrices with disjoint support; the edges are coloured by amicability and anti-amicability. Transversal-graph colour-complement existence conjecture. If a graph $T$ exists among the transversal graphs, then there exists at least one graph whose edge colours are complementary to those of $T$. This asserts existence of a colour-complementary transversal graph for every existing transversal graph; no resolution is given in the supplied material.