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\$\$Knfrom configurations of points in \$\$\backslashmathrm \PG\(2,q)\$\$PG(2,q). Here we provide an alternative procedure where the vertices of \$\$K_n\$\$Kncorrespond to the points of a hyperbola in \$\$\backslashmathrm \AG\(2,q)\$\$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.     «

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\$\$Knfrom configurations of points in \$\$\backslashmathrm \PG\(2,q)\$\$PG(2,q). Here we provide an alternative procedure where the vertices of \$\$K_n\$\$Kncorrespond to the points of a hyperbola in \$\$\backslashmathrm \AG\(2,q)\$\$AG(2,q). In this way, we obtain one-factorisations for parameters which a...     »