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Journal of Combinatorial Mathematics and Combinatorial Computing

  • Research article

Large Sets of Cycle Systems on Nine Points

Darryn Bryan1, Mike Grannell2, Terry Griggs2
1Centre for Discrete Mathematics and Computing Department of Mathematics The University of Queensland Queensland 4072 AUSTRALIA
2Department of Pure Mathematics The Open University Walton Hall Milton Keynes MK7 6AA UNITED KINGDOM
  • Published: 31/05/2005

Abstract

An \( m \)-cycle system of order \( v \), denoted by \( mCS(v) \), is a decomposition of the complete graph \( K_v \) into \( m \)-cycles. We discuss two types of large sets of \( mCS(v) \) and construct examples of both types for \( (m,v) = (4,9) \) and one type for \( (m,v) = (6,9) \). These are the first large sets of cycle systems constructed with \( m > 3 \), apart from the Hamiltonian cycle decompositions given in [2].

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Citation
Darryn Bryan, Mike Grannell, Terry Griggs. Large Sets of Cycle Systems on Nine Points[J], Journal of Combinatorial Mathematics and Combinatorial Computing, Volume 053. 95-102. DOI: .