Meirav Zehavi

Given a graph G and an integer k , the Interval Vertex Deletion (IVD) problem asks whether there exists a subset S ⊆ V ( G ) of size at most k such that G-S is an interval graph. This problem is known to be NP -complete (according to Yannakakis at STOC 1978). Originally in 2012, Cao and Marx showed that IVD is fixed parameter tractable: they exhibited an algorithm with running time 10 k n O (1). The existence of a polynomial kernel for IVD remained a well-known open problem in parameterized complexity. In this article, we settle this problem in the affirmative.