One-factorisations of complete graphs constructed in Desarguesian planes of certain odd square orders (Q2294105)
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| English | One-factorisations of complete graphs constructed in Desarguesian planes of certain odd square orders |
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One-factorisations of complete graphs constructed in Desarguesian planes of certain odd square orders (English)
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10 February 2020
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Summary: 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 \(\text{AGL}(1,q)\), points and ovals in the Desarguesian plane \(\text{PG}(2,q^2)\) to produce one-factorisations of the complete graph \(K_{q(q-1)} \).
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partial one-factorisation
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geometric one-factorisation of a complete graph
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