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Self-complementary graph decompositions

Part of: Designs and configurations Graph theory

Published online by Cambridge University Press:  09 April 2009

C. A. Rodger
C. A. Rodger
Affiliation:
120 Mathematics AnnexAuburn UniversityAuburn, AL 36849-5307, USA
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Abstract

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A complementary decomposition of λKn into a graph G is an edge-disjoint decomposition of λKn into copies of G such that if each copy H of G is replaced by its complement in V(H) then the result is an edge-disjoint decomposition of λKn into copies of GC it is a self- complementary decomposition if G = Gc. The spectrum for the last self-complementary graph on at most 7 vertices is found.

MSC classification

Secondary: 05B30: Other designs, configurations 05B40: Packing and covering 05C70: Factorization, matching, partitioning, covering and packing
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 53 , Issue 1 , August 1992 , pp. 17 - 24
Copyright
Copyright © Australian Mathematical Society 1992

References

[1]Bermond, J. C., Huang, C., Rosa, A. and Sotteau, D., ‘Decompositions of complete graphs into isomorphic subgraphs with five vertices,’ Ars Combinatoria 10 (1980), 211–254.Google Scholar
[2]Granville, A., Moisiadis, A. and Rees, R., ‘On Complementary Decompositions of the complete graph,’ Graphs and Combinatorics 5 (1989), 57–62.CrossRefGoogle Scholar
[3]Hanani, H., ‘Balanced incomplete block designs and related designs,’ Discrete Math. 11 (1975), 255–369.CrossRefGoogle Scholar
[4]Hoffman, D. G., Lindner, C. C. and Rodger, C. A., ‘On the construction of odd cycle systems,’ J. Graph Th. 13 (1989), 417–426.CrossRefGoogle Scholar
[5]Lindner, C. C. and Stinson, D. R., ‘Steiner pentagon systems,’ Discrete Math. 52 (1984), 67–74.CrossRefGoogle Scholar
[6]Rees, R. and Rodger, C. A., ‘Subdesigns in complementary path decompositions and incomplete two-fold designs with block size four,’ Ars Combinatoria, to appear.Google Scholar
[7]Rodger, C. A., ‘Graph decompositions,’ Le Matematiche 45, (1990), 119–139.Google Scholar
[8]Stinson, D. R., ‘The spectrum of nested Steiner triple systems,’ Graphs and Combinatorics 1 (1985), 189–191.CrossRefGoogle Scholar
[9]Street, A. P. and Street, D. J., Combinatorics of experimental design, Oxford Univ. Press, 1987.Google Scholar
[10]Tarsi, M., ‘Decompositions of complete multigraphs into stars,’ Discrete Math. 26 (1979), 273–278.CrossRefGoogle Scholar
[11]Tarsi, M., ‘Decompositions of complete multigraph into simple paths: non-balanced handcuff designs,’ J. Combinatorial Th. (A) 34 (1983), 60–70.CrossRefGoogle Scholar
[12]Zhu, L., ‘Existence of Holey Solssoms of Type 2n,’ Congressus Numerantiums 45 (1984), 295–304.Google Scholar
[13]Zhu, L., ‘A few more self-orthogonal latin squares with symmetric orthogonal mates,’ Proc. 13th Conf. on Num. Math. and Computing, University of Manitoba, 1983.Google Scholar