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Decomposing cubes

Part of: Graph theory

Published online by Cambridge University Press:  09 April 2009

P. Horak ,
J. Širáň  and
W. Wallis
P. Horak
Affiliation:
Slovak Technical University81219 Bratislava, Slovakia
J. Širáň
Affiliation:
Comenius University84215 Bratislava, Slovakia
W. Wallis
Affiliation:
Southern Illinois UniversityCarbondale Illinois 62901
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Abstract

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A graph H decomposes into a graph G if one can write H as an edge-disjoint union of graphs isomorphic to G. H decomposes into D, where D is a family of graphs, when H can be written as a union of graphs each isomorphic to some member of D, and every member of D is represented at least once. In this paper it is shown that the d-dimensional cube Qd decomposes into any graph G of size d each of whose blocks is either an even cycle or an edge. Furthennore, Qd decomposes into D, where D is any set of six trees of size d.

MSC classification

Secondary: 05C70: Factorization, matching, partitioning, covering and packing 05C99: None of the above, but in this section
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 61 , Issue 1 , August 1996 , pp. 119 - 128
Copyright
Copyright © Australian Mathematical Society 1996

References

[1]Dolinski, A. and Tarsi, M., ‘Graph decomposition is NPC — a complete proof of Holyer's conjecture.’, in: Proc. 24th annual ACM symposium on theory of computing (Victoria, BC, 1992) pp. 252–263.Google Scholar
[2]Fink, J. F., ‘On the decomposition of n-cubes into isomorphic trees’, J. Graph Theory 14 (1990), 405–411.CrossRefGoogle Scholar
[3]Jacobson, M. S., Truszczynski, M. and Tuza, Z., ‘Decompositions of regular bipartite graphs’, Discrete Math. 89 (1991), 17–27.CrossRefGoogle Scholar
[4]Ringel, G., ‘Problem 25’, in: Theory of graphs and its applications (Smolenice, 1963) (Czechoslovak Academy of Science, Prague, 1964) p. 162.Google Scholar
[5]Wilson, R. M., ‘Decompositions of complete graphs into subgraphs’, Congr. Numer. 15 (1976), 647–659.Google Scholar