Geodesic
One-factorisations of complete graphs constructed in Desarguesian planes of certain odd square orders
Nicola Pace1 ; Angelo Sonnino2
1Technical University of Munich
2Università degli Studi della Basilicata
The electronic journal of combinatorics, Tome 27 (2020) no. 1
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A geometric construction of one-factorisations of complete graphs $K_{q(q-1)}$ is provided for the case when either $q=2^d +1$ is a Fermat prime, or $q=9$. This construction uses the affine group $\mathrm{AGL}(1,q)$, points and ovals in the Desarguesian plane $\mathrm{PG}(2,q^{2})$ to produce one-factorisations of the complete graph $K_{q(q-1)}$.
DOI : 10.37236/8378
Classification : 05C70, 51E21, 05B25
Mots-clés : partial one-factorisation, geometric one-factorisation of a complete graph

Nicola Pace  1   ; Angelo Sonnino  2

1 Technical University of Munich
2 Università degli Studi della Basilicata 
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     title = {One-factorisations of complete graphs constructed in {Desarguesian} planes of certain odd square orders},
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Nicola Pace; Angelo Sonnino. One-factorisations of complete graphs constructed in Desarguesian planes of certain odd square orders. The electronic journal of combinatorics, Tome 27 (2020) no. 1. doi: 10.37236/8378

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