On circular–linear one-factorizations of the complete graph

In Korchmáros et al. (2018)one-factorizations of the complete graph Kn are constructed for n=q+1 with any odd prime power q such tha teither q≡1 (mod4) or q=2h−1. The arithmetic restriction n = q + 1 is due to the fact that the vertices of Kn in the construction are the points of a conic Ω in the finite plane of order q. Here we work on the Euclidean plane and describe an analogous construction where the role of Ω is taken by a regular n-gon. This allows us to remove the above constraints and construct one-factorizations of Kn for every even n ≥ 6.