Elimination distance to bounded degree on planar graphs
It resolves the parameterized complexity of this graph parameter on planar graphs, which is relevant for graph isomorphism and structural graph theory.
The paper proves that the elimination distance to bounded degree problem is fixed-parameter tractable on planar graphs, providing an algorithm with runtime f(k,d)·n^c.
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 $k$.