A polynomial kernel for proper Helly circular-arc vertex deletion

A proper Helly circular-arc graph is an intersection graph of a set of arcs on a circle such that none of the arcs properly contains any other arc and every set of pairwise intersecting arcs has a common intersection. The Proper Helly Circular-arc Vertex Deletion problem takes as input a graph G and an integer k , and the goal is to check if we can remove at most k vertices from the graph to obtain a proper Helly circular-arc graph; the parameter is k . Recently, Cao et al. [MFCS 2023] obtained an FPT algorithm for this (and related) problem. In this work, we obtain a polynomial kernel for the problem.