Polynomial Kernel for Interval Vertex Deletion

Akanksha Agrawal, Daniel Lokshtanov, Pranabendu Misra, Saket Saurabh, Meirav Zehavi

Abstract: 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 10k nO(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.