Hostname: page-component-848d4c4894-ndmmz Total loading time: 0 Render date: 2024-05-16T08:19:37.382Z Has data issue: false hasContentIssue false
  • English
  • Français

Decompositions of complete symmetric digraphs into the oriented pentagons

Part of: Graph theory

Published online by Cambridge University Press:  09 April 2009

Brian Alspach ,
Katherine Heinrich  and
Badri N. Varma
Brian Alspach
Affiliation:
Department of Mathematics Simon Fraser UniversityByrnaby, B.C. V51 1A6, Canada
Katherine Heinrich
Affiliation:
University of Newcastle and University of Arizona
Badri N. Varma
Affiliation:
Simon Fraser University
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We show that the complete symmetric digraph DKn, n≧5, can be decomposed into each of the four oriented pentagons if and only if n ≡ 0 or 1 (mod 5).

MSC classification

Secondary: 05C20: Directed graphs (digraphs), tournaments 05C38: Paths and cycles
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 28 , Issue 3 , November 1979 , pp. 353 - 361
Copyright
Copyright © Australian Mathematical Society 1979

References

Behzad, M. and Chartrand, G. (1971), Introduction to the theory of graphs (Allyn & Bacon, Boston).Google Scholar
Bermond, J.-C. and Sotteau, D. (1975), ‘Graph decomposition and G-designs, Proc. 5th British Combinatorial Conference, Utilitas Math. (Winnipeg), Cong. Num. 15, 53–72.Google Scholar
Bermond, J.-C. and Sotteau, D. (1977), ‘Cycle and circuit designs odd case’, Proc. International Colloquium of Oberhof, 11–32.Google Scholar
Harary, F., Palmer, E. M. and Smith, C. A. B. (1967), ‘Which graphs have only self-converse orientations?’ Canad. Math. Bull. 10, 425–429.CrossRefGoogle Scholar
Harary, F. (1969), Graph theory (Addison-Wesley, Reading, Mass.).CrossRefGoogle Scholar
Harary, F., Heinrich, Katherine and Wallis, W. D. (1978), ‘Decompositions of complete symmetric digraphs into the four oriented quadrilaterals’, Proc. International Combinatorics Conf. (Camberra) (Lecture dotes in mathematics 686, Springer-Verlag, 165–173).Google Scholar
Hung, S. H. Y. and Mendelsohn, N. S. (1973), ‘Directed triple systems’, J. Combinatorial Theory, Ser. B 14, 310–318.CrossRefGoogle Scholar
Rosa, A. and Huang, C. (1975), ‘Another class of balanced graph designs: balanced circuit designs’, Discrete Math. 11, 67–70.Google Scholar
Spencer, J. (1968), ‘Maximal consistent families of triples’, J. Combinatorial Theory 5, 1–8.CrossRefGoogle Scholar
Wilson, R. M. (1974), ‘Some partitions of all triples into Steiner triple sysetms’, Hypergraph seminar (Lecture notes in mathematics 411, Springer-Verlag, 267–277).CrossRefGoogle Scholar