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New families of atomic Latin squares and perfect 1-factorisations

Bryant, D, Maenhaut, B and Wanless, IM (2006). New families of atomic Latin squares and perfect 1-factorisations. Journal of Combinatorial Theory Series A,113(4):608-624.

Document type: Journal Article
Citation counts: Scopus Citation Count Cited 5 times in Scopus Article | Citations

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Title New families of atomic Latin squares and perfect 1-factorisations
Author Bryant, D
Maenhaut, B
Wanless, IM
Journal Name Journal of Combinatorial Theory Series A
Publication Date 2006
Volume Number 113
Issue Number 4
ISSN 0097-3165   (check CDU catalogue open catalogue search in new window)
Scopus ID 2-s2.0-33645542951
Start Page 608
End Page 624
Total Pages 17
Place of Publication Orlando
Publisher Academic Press
HERDC Category C1 - Journal Article (DEST)
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 dernonstrate 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 K (p,p). If 2 is a primitive root modulo p, then we show the existence of 11 non-isomorphic: perfect 1-factorisations of K-p,(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. (c) 2005 Elsevier Inc. All rights reserved.
Keywords perfect 1-factorisation
atomic latin square
totally symmetric
hamiltonian cycle
even starter
autotopy group
symmetry groups
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Created: Wed, 28 Nov 2007, 14:16:08 CST