國立臺灣大學數學系Hwang, F.K.F.K.HwangChang, G.J.G.J.Chang2006-09-272018-06-282006-09-272018-06-281998http://ntur.lib.ntu.edu.tw//handle/246246/20060927121114414875Consecutive & 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.application/pdf118553 bytesapplication/pdfzh-TWjournal articlehttp://ntur.lib.ntu.edu.tw/bitstream/246246/20060927121114414875/1/045.pdf