Before revision:  We then turn to a statistical approach to the question by studying the rigidity and connectivity of kirigami with random cuts , and find that both the T and DoF can be exquisitely controlled by the density of cuts (links) in the neighborhood of percolation transitions in the connectivity and rigidity.
After revision:  We then turn to a statistical approach to the question by studying the rigidity and connectivity of kirigami with random cuts , and find that both the number of connected pieces and the degrees of freedom show percolation transitions as a function of the density of cuts (links) in the neighborhood of percolation transitions in the connectivity and rigidity.