Modification Problems toward Proper (Helly) Circular-arc Graphs

02/02/2022

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by   Yixin Cao, et al.

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We present a 9^k· 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.