Akansha Agrawal, Polynomial Kernel for Interval Vertex Deletion

Given a graph G and an integer k, the Interval Vertex Deletion (IVD) problem asks whether there exists a vertex subset S of size at most k, such that G-S is an interval graph. A polynomial kernel for a parameterized problem is a polynomial time preprocessing algorithm that outputs an equivalent instance of the problem whose size is bounded by a polynomial function of the parameter. The existence of a polynomial kernel for IVD remained a well-known open problem in Parameterized Complexity. In this talk we look at a sketch of a polynomial kernel for the problem (with the solution size as the parameter). To illustrate one of the key ingredients of our kernel, we will look at a polynomial kernel for IVD, when parameterized by the vertex cover number.