Perfect 1-factorisations of $K_{16}$
Combinatorics
2020-04-30 v1
Abstract
We report the results of a computer enumeration that found that there are 3155 perfect 1-factorisations (P1Fs) of the complete graph . 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 , (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.
Keywords
Cite
@article{arxiv.1905.07535,
title = {Perfect 1-factorisations of $K_{16}$},
author = {Michael J. Gill and Ian M. Wanless},
journal= {arXiv preprint arXiv:1905.07535},
year = {2020}
}