Polynomial kernel for immersion hitting in tournaments

TL;DR

This paper proves that for any fixed simple digraph H, the problem of removing arcs from a tournament to eliminate H as an immersion has a polynomial kernel, with size depending on H.

Contribution

It establishes the existence of a polynomial kernel for the immersion hitting problem in tournaments for any fixed digraph H.

Findings

Polynomial kernel exists for the problem when parameterized by the number of arc deletions.

Kernel size bound depends on the structure of H.

The result applies to all fixed simple digraphs without isolated vertices.

Abstract

For a fixed simple digraph $H$ without isolated vertices, we consider the problem of deleting arcs from a given tournament to get a digraph which does not contain $H$ as an immersion. We prove that for every $H$, this problem admits a polynomial kernel when parameterized by the number of deleted arcs. The degree of the bound on the kernel size depends on $H$.