One-factorisations of complete graphs arising from hyperbolae in the Desarguesian affine plane

In a recent paper Korchmáros et al. (J Combin Theory Ser A 160:62–83, 2018) the geometry of finite planes is exploited for the construction of one-factorisations of the complete graph K n from configurations of points in PG (2 , q). Here we provide an alternative procedure where the vertices of K n correspond to the points of a hyperbola in AG (2 , q). In this way, we obtain one-factorisations for parameters which are either not covered by the constructions in Korchmáros et al. (J Combin Theory Ser A 160:62–83, 2018), or isomorphic to known examples but arising from different geometric configurations.