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arXiv · 1905.07535

Perfect 1-factorisations of $K_{16}$

Michael J. Gill·Ian M. Wanless
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Abstract

We report the results of a computer enumeration that found that there are 3155 perfect 1-factorisations (P1Fs) of the complete graph $K_{16}$. Of these, 89 have a non-trivial automorphism group (correcting an earlier claim of 88 by Meszka and Rosa). We also (i) describe a new invariant which distinguishes between the P1Fs of $K_{16}$, (ii) observe that the new P1Fs produce no atomic Latin squares of order 15 and (iii) record P1Fs for a number of large orders that exceed prime powers by one.

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Michael J. Gill, Ian M. Wanless. 2019-05-18. Perfect 1-factorisations of $K_{16}$. https://doi.org/10.1017/s0004972719000856

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