A Polynomial Kernel for Proper Helly Circular-Arc Vertex Deletion

Akanksha Agrawal, Satyabrata Jana, Abhishek Sahu

Abstract: 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.