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

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Abstract

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 \(\mathrm {PG}(2,q)\). 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 Korchmáros et al. (J Combin Theory Ser A 160:62–83, 2018), or isomorphic to known examples but arising from different geometric configurations.

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Acknowledgements

This research was carried out within the activities of the GNSAGA—Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni of the Italian INdAM. Nicola Pace was supported by the Alexander von Humboldt Foundation with funds from the German Federal Ministry of Education and Research (BMBF).

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Authors and Affiliations

  1. Chair of Operations Research, Technical University of Munich, Arcisstr. 21, 80333, Munich, Germany

    Nicola Pace

  2. Dipartimento di Matematica, Informatica ed Economia, Università degli Studi della Basilicata, Viale dell’Ateneo Lucano 10, 85100, Potenza, Italy

    Angelo Sonnino

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  1. Nicola Pace
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  2. Angelo Sonnino
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Correspondence to Nicola Pace.

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Pace, N., Sonnino, A. One-factorisations of complete graphs arising from hyperbolae in the Desarguesian affine plane. J. Geom. 110, 15 (2019). https://doi.org/10.1007/s00022-019-0470-6

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  • DOI: https://doi.org/10.1007/s00022-019-0470-6

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