5-Cycle Systems with Holes

  • Darryn E. Bryant
  • D. G. Hoffman
  • C. A. Rodger

Abstract

Recently the generalized Doyen-Wilson problem of embedding a 5-cycle system of order u in one of order υ was completely solved. However it is often useful to solve the more general problem of the existence of a 5-cycle system of order υ with a hole of size u. In this paper we completely solve this problem.

Keywords

Congo 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    D. E. Bryant and C. A. Rodger, On the Doyen-Wilson Theorem for m-cycle systems, J. Combin. Designs, Vol. 2 (1994) pp. 253–271.MathSciNetMATHCrossRefGoogle Scholar
  2. 2.
    D. E. Bryant and C. A. Rodger, The Doyen-Wilson Theorem extended to 5-cycles, J. Combin. Theory Ser. A, Vol. 68 (1994) pp. 218–224.MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    J. Doyen and R. M. Wilson, Embeddings of Steiner triple systems, Discrete Math, Vol. 5 (1973) pp. 229–239.MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    D. G. Hoffman and C. A. Rodger, The chromatic index of complete multipartite graphs, J. Graph Theory, Vol. 16 (1992) pp. 159–163.MathSciNetMATHCrossRefGoogle Scholar
  5. 5.
    C. A. Rodger, Problems on cycle systems of odd length, Cong. Numer., Vol. 61 (1988) pp. 5–22.MathSciNetGoogle Scholar
  6. 6.
    E. Mendelsohn and A. Rosa, Embedding maximum packings of triples, Cong. Numer., Vol. 40 (1983) pp. 235–247.MathSciNetGoogle Scholar
  7. 7.
    G. Stern and A. Lenz, Steiner triple systems with given subspaces; another proof of the Doyen-Wilson theorem, Boll. Un. Mat. Ital. A (5), Vol. 17 (1980) pp. 109–114.MathSciNetMATHGoogle Scholar

Copyright information

© Kluwer Academic Publishers, Boston 1996

Authors and Affiliations

  • Darryn E. Bryant
    • 1
  • D. G. Hoffman
    • 2
  • C. A. Rodger
    • 2
  1. 1.Centre for Combinatorics, Department of MathematicsThe University of QueenslandAustralia
  2. 2.Department of Discrete and Statistical SciencesAuburn UniversityAuburnUSA

Personalised recommendations