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On isopart parameters of complete bipartite graphs and n-cubes. (English) Zbl 0585.05027
A graph H is said to be G-decomposable if H can be decomposed into the subgraphs \(H_ 1,H_ 2,...,H_ n\) such that they are all isomorphic to G. Fink introduced three ”isopart parameters”, \(p_ 0(G)\), \(r_ 0(G)\), and \(f_ 0(G)\). The numbers \(p_ 0(G)\) and \(r_ 0(G)\) are respectively the minimum order and minimum degree of regularity among all connected, regular, G-decomposable graphs. The parameter \(f_ 0(G)\) is the smallest number t (\(\geq 2)\) for which there exists a connected regular graph H decomposable into t copies of G. The authors determine the three parameters for all complete bipartite graphs and the n-cube.
Reviewer: Z.Ma
MSC:
05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)
05C99 Graph theory
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References:
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