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The cutwidth of a graph G is the minimum number of overlap edges when G is embedded into a path Pn. The cutwidth problem for a graph G is to determine the cutwidth of G. A graph G with cutwidth k is k-cutwidth critical if every proper subgraph of G has cutwidth less than k and G is homeomorphically minimal. In this paper, we completely investigated methods of forming a k-cutwidth(k > 1) critical tree T.  相似文献   
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