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

Abstract

In a recent paper Korchmaros 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 $$\mathrm {PG}(2,q)$$ . Here we provide an alternative procedure where the vertices of $$K_n$$ correspond to the points of a hyperbola in $$\mathrm {AG}(2,q)$$ . In this way, we obtain one-factorisations for parameters which are either not covered by the constructions in Korchmaros et al. (J Combin Theory Ser A 160:62–83, 2018), or isomorphic to known examples but arising from different geometric configurations.