Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-11-26T03:03:09.048Z Has data issue: false hasContentIssue false
  • English
  • Français

GENERALISATIONS OF THE DOYEN–WILSON THEOREM

Part of: Designs and configurations Graph theory

Published online by Cambridge University Press:  04 December 2017

ROSALIND A. HOYTE
ROSALIND A. HOYTE*
Affiliation:
Department of Mathematics and Statistics, Memorial University of Newfoundland, St John’s, NL, CanadaA1C 5S7 email [email protected]
Rights & Permissions [Opens in a new window]

Abstract

An abstract is not available for this content so a preview has been provided. As you have access to this content, a full PDF is available via the ‘Save PDF’ action button.
Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'

Keywords

Doyen–Wilson theoremcycle systemsubsystemgraph decompositioncomplete graph with a holecycle switching

MSC classification

Primary: 05C70: Factorization, matching, partitioning, covering and packing
Secondary: 05B30: Other designs, configurations 05C38: Paths and cycles
Type
Abstracts of Australasian PhD Theses
Information
Bulletin of the Australian Mathematical Society , Volume 97 , Issue 1 , February 2018 , pp. 166 - 167
Copyright
© 2017 Australian Mathematical Publishing Association Inc. 

References

Alspach, B. and Gavlas, H., ‘Cycle decompositions of K n and K n - I ’, J. Combin. Theory Ser. B 81(1) (2001), 77–99.Google Scholar
Bryant, D. E., Horsley, D., Maenhaut, B. M. and Smith, B. R., Decompositions of complete multigraphs into cycles of varying lengths’, Preprint, 2015, arXiv:1508.00645 [math.CO].Google Scholar
Bryant, D. E., Horsley, D. and Pettersson, W., ‘Cycle decompositions V: Complete graphs into cycles of arbitrary lengths’, Proc. Lond. Math. Soc. (3) 108(5) (2014), 1153–1192.Google Scholar
Bryant, D. E. and Rodger, C. A., ‘The Doyen–Wilson theorem extended to 5-cycles’, J. Combin. Theory Ser. A 68(1) (1994), 218–225.Google Scholar
Bryant, D. E., Rodger, C. A. and Spicer, E. R., ‘Embeddings of m-cycle systems and incomplete m-cycle systems: m ≤ 14’, Discrete Math. 171(1–3) (1997), 55–75.Google Scholar
Chou, C.-C., Fu, C.-M. and Huang, W.-C., ‘Decomposition of K m, n into short cycles’, Discrete Math. 197/198 (1999), 195–203.CrossRefGoogle Scholar
Doyen, J. and Wilson, R. M., ‘Embeddings of Steiner triple systems’, Discrete Math. 5 (1973), 229–239.CrossRefGoogle Scholar
Horsley, D., ‘Decomposing various graphs into short even-length cycles’, Ann. Comb. 16(3) (2012), 571–589.Google Scholar
Mendelsohn, E. and Rosa, A., ‘Embedding maximal packings of triples’, Congr. Numer. 40 (1983), 235–247.Google Scholar
Šajna, M., ‘Cycle decompositions III. Complete graphs and fixed length cycles’, J. Combin. Des. 10(1) (2002), 27–78.Google Scholar