In this paper, we consider the problem of finding an induced cycle passing through k given vertices, which we call the induced cycle problem. The significance of finding induced cycles stems from the fact that a precise characterization of perfect graphs would require understanding the structure of graphs without an odd induced cycle and its complement. There has been huge progress in the recent years, especially, the Strong Perfect Graph Conjecture was solved in [6]. Concerning recognition of perfect graphs, there had been a long-standing open problem for detecting an odd hole and its complement, and finally this was solved in [4].
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