Perfect 1-factorisations of $K_{16}$

Abstract

We report the results of a computer enumeration that found that there are 3155 perfect 1factorisations (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 [6]).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.