## 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 [Yannakakis, STOC’78]. 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)} [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.

Original language | English |
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Pages | 1711-1730 |

Number of pages | 20 |

DOIs | |

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

Conference | 30th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2019 |
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Country/Territory | United States |

City | San Diego |

Period | 6/01/19 → 9/01/19 |

## ASJC Scopus subject areas

- Software
- General Mathematics