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**Covering and packing in graphs. V. Mispacking subcubes in hypercubes.**
*(English)*
Zbl 0645.05058

A node-disjoint packing of a graph G with a subgraph H is a largest collection of disjoint copies of a smaller graph H contained in G; an edge disjoint packing is defined similarly, but no two copies of H have a common edge. Two packing numbers of G with H are defined accordingly. It is easy to determine both of these numbers when H is a subcube of a hypercube G. A mispacking of G with subgraphs H is a minimum maximal collection of disjoint copies of H whose removal from G leaves no subgraph H. Two mispacking numbers of G and H are defined analogously to the packing numbers. Their exact determination is quite difficult but we obtain upper bounds. The covering number of G by a subgraph H is the smallest number of copies of H whose union is all of G. This number is determined for \(G=Q_ n\), \(H=Q_ m\).

### MSC:

05C70 | Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) |

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\textit{N. Graham} and \textit{F. Harary}, Comput. Math. Appl. 15, No. 4, 267--270 (1988; Zbl 0645.05058)

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### References:

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[2] | Akiyama, J.; Exoo, G.; Harary, F., Covering and packing in graphs IV: linear arboricity, Networks, 11, 69-72, (1981) · Zbl 0479.05027 |

[3] | Harary, F., () |

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[5] | J. P. Hayes, T. N. Mudge, Q. F. Stout, S. Colley and J. Palmer. Architecture of a hypercube supercomputer. Proc. 1986 Int. Conf. on Parallel Processing. St. Charles, Illinois (to appear). |

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