Induced H-packing k-partition problem in interconnection networks

ABSTRACT The induced matching k-partition number of a graph G, denoted by , is the minimum integer k such that has a k-partition where for each i, , , the subgraph of G induced by , is a 1-regular graph. The induced matching k-partition problem is NP-complete even for k = 2. In this paper we extend the concept of matching to H-packing and denote the minimum induced H-packing k-partition number as . We prove that the induced -packing k-partition problem and induced -packing k-partition problem are both NP-complete problems. We obtain the induced -packing k-partition number for sierpiński graphs and hypercube networks. Further we determine the induced -packing k-partition number for hypercube networks.

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