Elimination distance to bounded degree on planar graphs

TL;DR

This paper proves that determining the elimination distance to bounded degree is fixed-parameter tractable on planar graphs, enabling efficient algorithms for this graph parameter.

Contribution

It establishes the fixed-parameter tractability of the elimination distance to bounded degree on planar graphs, advancing understanding of graph isomorphism complexity.

Findings

The problem is fixed-parameter tractable on planar graphs.

An algorithm exists with runtime f(k,d)·n^c for deciding elimination distance.

The result applies to the class of degree d graphs.

Abstract

We study the graph parameter elimination distance to bounded degree, which was introduced by Bulian and Dawar in their study of the parameterized complexity of the graph isomorphism problem. We prove that the problem is fixed-parameter tractable on planar graphs, that is, there exists an algorithm that given a planar graph $G$ and integers $d$ and $k$ decides in time $f(k,d)\cdot n^c$ for a computable function~$f$ and constant $c$ whether the elimination distance of $G$ to the class of degree $d$ graphs is at most $k$.