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Decomposition of Kn into Dragons

Published online by Cambridge University Press:  20 November 2018

C. Huang  and
J. Schonheim
C. Huang
Affiliation:
Carleton University, Ottawa, K1S 5B6, Department of Mathematical Sciences, Tel-Aviv University, Tel-Aviv
J. Schonheim
Affiliation:
Carleton University, Ottawa, K1S 5B6, Department of Mathematical Sciences, Tel-Aviv University, Tel-Aviv
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Abstract

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It is shown that if 1<n ≡ 0 or 1 (mod 2 m), then the edges of Kn may be partitioned into isomorphic copies of a graph D3(m) and also of a graph D4(m), graphs consisting respectively of a triangle with an attached path of m - 3 edges or a quadrilateral with an attached path of m - 4 edges. If m is a power of 2 then the above condition is shown to be necessary and sufficient for the existence of such a partition.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 23 , Issue 3 , 01 September 1980 , pp. 275 - 279
Copyright
Copyright © Canadian Mathematical Society 1980

References

1. Bermond, J.C. and Schonheim, J., G-decomposition of Kn, where G has four vertices or less, Discrete Mathematics 19 (1977) 113-120.Google Scholar
2. Rosa, A. and Huang, C., Another class of Balanced graph designs, Balanced Circuit Designs, Discrete Mathematics 12 (1975) 269-293.Google Scholar
3. Skolem, Th., On certain distribution of integers in pairs with given differences, Math. Scand. 5 (1957) 57-68.Google Scholar