1 results
PERFECT 1-FACTORISATIONS OF
$K_{16}$
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 101 / Issue 2 / April 2020
- Published online by Cambridge University Press:
- 07 August 2019, pp. 177-185
- Print publication:
- April 2020
-
- Article
- Export citation
-
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 nontrivial automorphism group (correcting an earlier claim of 88 by Meszka and Rosa [‘Perfect 1-factorisations of 
$K_{16}$ with nontrivial automorphism group’, J. Combin. Math. Combin. Comput. 47 (2003), 97–111]). 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.
