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Minimal Decompositions of Complete Graphs into Subgraphs with Embeddability Properties

Published online by Cambridge University Press:  20 November 2018

L. W. Beineke
L. W. Beineke*
Affiliation:
Purdue University, Fort Wayne, Indiana
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Although the problem of finding the minimum number of planar graphs into which the complete graph can be decomposed remains partially unsolved, the corresponding problem can be solved for certain other surfaces. For three, the torus, the double-torus, and the projective plane, a single proof will be given to provide the solutions. The same questions will also be answered for bicomplete graphs.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 21 , 1969 , pp. 992 - 1000
Copyright
Copyright © Canadian Mathematical Society 1969

References

1. Beineke, L. W. and Harary, F., The thickness of the complete graph, Can. J. Math. 17 (1965), 850–859.Google Scholar
2. Beineke, L. W., Harary, F., and Moon, J. W., On the thickness of the complete bipartite graph Proc. Cambridge Philos. Soc. 60 (1964), 1–5 Google Scholar
3. Franklin, P., A six-color problem, J. Math. Phys. 13 (1934), 363–369.Google Scholar
4. Ringel, G., Die toroidale Dicke des vollstdndigen Graphen, Math. Z. 87 (1965), 19–26.Google Scholar