New families of atomic Latin squares and perfect 1-factorisations

D Bryant, B Maenhaut, Ian Murray Wanless

    Research output: Contribution to journalComment/debate

    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.
    Original languageEnglish
    Pages (from-to)608-624
    Number of pages17
    JournalJournal of Combinatorial Theory Series A
    Volume113
    Issue number4
    DOIs
    Publication statusPublished - 2006

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