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A new graph parameter, called tree-coritivity, is introduced in this paper. A decycling-cut is a vertex-cut whose removal results in an acyclic graph. Let ω(G) be the number of connected components of a graph G. The tree-coritivity of a graph G is the maximum value of ω(G−S⁎)−|S⁎|, where S⁎ takes over all decycling-cuts of G. It is shown that this parameter can be used to measure the vulnerability...
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