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 [Yannakakis, STOC’78]. Originally in 2012, Cao and Marx showed that IVD is fixed parameter tractable: they exhibited an algorithm with running time 10knO(1) [Cao and Marx, SODA’14]. The existence of a polynomial kernel for IVD remained a well-known open problem in Parameterized Complexity. In this paper, we settle this problem in the affirmative. We also introduce a “bounded intersection” variant of the classical Two Families theorem of Bollobás. We believe this result will find further applications in combinatorics and algorithm design.
|Number of pages||20|
|State||Published - 1 Jan 2019|
|Event||30th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2019 - San Diego, United States|
Duration: 6 Jan 2019 → 9 Jan 2019
|Conference||30th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2019|
|Period||6/01/19 → 9/01/19|