The complementary prism \(G{\overline{G}}\) is the graph obtained by taking a copy of a simple graph G and a copy of its complement \({\overline{G}}\) , and then linking with an edge each pair of corresponding vertices. In 2019, it was shown that every non-regular complementary prism \(G{\overline{G}}\) is Class 1 (i.e. \(\Delta (G{\overline{G}})\) -edge-colourable), and it was conjectured that the Petersen graph is the only Class 2 (i.e. not Class 1) complementary prism. We provide further evidence for this conjecture by showing that asymptotically almost every \(d\) -regular complementary prism has at least \(4\lfloor h / 3\rfloor + (h \bmod 3)\) pairwise-disjoint perfect matchings, being \(h =(d - 3) / 2\) .
