Publication:
Enumerating Consecutive and Nested Partitions for Graphs

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1998

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Hwang, F.K.
Hwang, F.K.; Chang, G.J.
Chang, G.J.

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Research Projects

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Consecutive & nested partitions have been extensively studied in the set-partition problem as tools with which to search efficiently for an optimal partition. We extend the study of consecutive and nested partitions on a set of integers to the vertex-set of a graph. A subset of vertices is considered consecutive if the subgraph induced by the subset is connected. In this sense the partition problem on a set of integers can be treated as a special case when the graph is a line. In this paper we give the number of consecutive & nested partitions when the graph is a cycle. We also give a partial order on general graphs with respect to these numbers.

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