One-factorizations of the complete graph Kn have wide applications, as an example they are often used for scheduling round-robin tournaments with n teams. In this note, we characterize parabolic and linear one-factorizations of complete graphs Kp+1, when p is an odd prime. This class of one-factorizations arises from the geometry of conics and lines in the affine plane AG(2, p). We also include Magma computations for the cases p ≤ 19.
A note on parabolic and linear one-factorizations of the complete graph Kp+1
Smaldore V.
2024
Abstract
One-factorizations of the complete graph Kn have wide applications, as an example they are often used for scheduling round-robin tournaments with n teams. In this note, we characterize parabolic and linear one-factorizations of complete graphs Kp+1, when p is an odd prime. This class of one-factorizations arises from the geometry of conics and lines in the affine plane AG(2, p). We also include Magma computations for the cases p ≤ 19.
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