Round-dance neighbour designs from terraces

Rosemary Anne Bailey, M. A. Ollis, D. A. Preece

Research output: Contribution to journalArticlepeer-review

27 Citations (Scopus)

Abstract

In a round-dance neighbour design, an odd number v of objects is arranged successively in (v-1)/2 rings (circular blocks) such that any two of the objects are adjacent to one another in exactly one ring. A round-dance neighbour design is also a Hamiltonian decomposition of the complete graph on v vertices. We show how such designs can be constructed from terraces, which are building blocks for row-complete Latin squares. A round-dance neighbour design is equivalent to a Tuscan square in which the reverse of each row is also a row. Terraces for the cyclic group of order n are used to construct elegantly patterned round-dance neighbour designs for n2^m + 1 objects for any positive integer m.
Original languageEnglish
Pages (from-to)69-86
Number of pages18
JournalDiscrete Mathematics
Volume266
Publication statusPublished - 2003

Keywords

  • 2-sequencings
  • balanced-circuit designs
  • directed terraces
  • Hamiltonian decomposition
  • Lucas-Walecki construction
  • Owens terrace
  • Ramsgate Sands problem
  • Rees neighbour designs
  • row-complete Latin squares
  • symmetric sequencings
  • triangular-numbers terraces
  • Tuscan squares

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