New families of atomic Latin squares and perfect 1-factorisations

Bryant, Darryn, Maenhaut, Barbara and Wanless, Ian M. (2006) New families of atomic Latin squares and perfect 1-factorisations. Journal of Combinatorial Theory Series A, 113 4: 608-624. doi:10.1016/j.jcta.2005.05.003

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Author Bryant, Darryn
Maenhaut, Barbara
Wanless, Ian M.
Title New families of atomic Latin squares and perfect 1-factorisations
Journal name Journal of Combinatorial Theory Series A   Check publisher's open access policy
ISSN 0097-3165
Publication date 2006-05-01
Sub-type Article (original research)
DOI 10.1016/j.jcta.2005.05.003
Volume 113
Issue 4
Start page 608
End page 624
Total pages 17
Editor H. Barcelo
Place of publication New York, NY, U.S.A.
Publisher Academic Press
Language eng
Subject C1
230101 Mathematical Logic, Set Theory, Lattices And Combinatorics
780101 Mathematical sciences
0101 Pure Mathematics
Formatted abstract
A perfect 1-factorisation of a graph G is a decomposition of G into edge disjoint 1-factors such that the union of any two of the factors is a Hamiltonian cycle. Let p≥11 be prime. We demonstrate the existence of two non-isomorphic perfect 1-factorisations of Kp+1 (one of which is well known) and five non-isomorphic perfect 1-factorisations of Kp,p. If 2 is a primitive root modulo p, then we show the existence of 11 non-isomorphic perfect 1-factorisations of Kp,p and 5 main classes of atomic Latin squares of order p. Only three of these main classes were previously known. One of the two new main classes has a trivial autotopy group.
© 2005 Elsevier Inc. All rights reserved.
Keyword Perfect 1-factorisation
Atomic Latin square
Totally symmetric
Hamiltonian cycle
Even starter
Autotopy group
Symmetry groups
Q-Index Code C1

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Citation counts: TR Web of Science Citation Count  Cited 8 times in Thomson Reuters Web of Science Article | Citations
Scopus Citation Count Cited 11 times in Scopus Article | Citations
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Created: Wed, 15 Aug 2007, 18:57:58 EST