Modification Problems toward Proper (Helly) Circular-arc Graphs

We present a $9^k\cdot n^{O(1)}$-time algorithm for the proper circular-arc vertex deletion problem, resolving an open problem of van 't Hof and Villanger [Algorithmica 2013] and Crespelle et al. [arXiv:2001.06867]. Our structural study also implies parameterized algorithms for modification problems toward proper Helly circular-arc graphs.