A Polynomial kernel for Proper Interval Vertex Deletion

TL;DR

This paper proves that the Proper Interval Vertex Deletion problem admits a polynomial kernel, resolving an open question and advancing the understanding of fixed parameter tractability in graph modification problems.

Contribution

The paper establishes the existence of a polynomial kernel for Proper Interval Vertex Deletion, a previously open problem in parameterized complexity.

Findings

Established a polynomial kernel for Proper Interval Vertex Deletion

Resolved an open question in fixed parameter tractability

Advances understanding of graph modification problems

Abstract

It is known that the problem of deleting at most k vertices to obtain a proper interval graph (Proper Interval Vertex Deletion) is fixed parameter tractable. However, whether the problem admits a polynomial kernel or not was open. Here, we answers this question in affirmative by obtaining a polynomial kernel for Proper Interval Vertex Deletion. This resolves an open question of van Bevern, Komusiewicz, Moser, and Niedermeier.