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. All together, our work provides a general framework for the topological and statistical control of rigidity and connectivity in planar kirigami.
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 T and DoF can be exquisitely controlled by the density of cuts (links) . Together this provides a general framework for the topological and statistical control of rigidity and connectivity in planar kirigami.