Perfect 1-factorisations of K16

Michael J. Gill, Ian A.N.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 K16. Of these, 89 have a nontrivial automorphism group (correcting an earlier claim of 88 by Meszka and Rosa ['Perfect 1-factorisations of K16 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 K16, (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.

Original languageEnglish
Pages (from-to)177-185
Number of pages9
JournalBulletin of the Australian Mathematical Society
Volume101
Issue number2
DOIs
Publication statusPublished - Apr 2020

Keywords

  • atomic Latin square
  • Hamilton cycle
  • Perfect 1-factorisation
  • quotient coset starter
  • train

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