Solving Dominating Set in Larger Classes of Graphs: FPT Algorithms and Polynomial Kernels

TL;DR

This paper proves that the k-Dominating Set problem is fixed parameter tractable and admits polynomial kernels for a broad class of graphs excluding certain bipartite subgraphs, extending previous results and solving an open problem.

Contribution

It establishes FPT algorithms and polynomial kernels for k-Dominating Set in graphs excluding K_{i,j}, including bounded-degenerate graphs, broadening the scope of known tractable cases.

Findings

FPT algorithms for k-Dominating Set in graphs excluding K_{i,j}

Polynomial kernels for these graph classes

Solves an open problem for bounded-degenerate graphs

Abstract

We show that the k-Dominating Set problem is fixed parameter tractable (FPT) and has a polynomial kernel for any class of graphs that exclude K_{i,j} as a subgraph, for any fixed i, j >= 1. This strictly includes every class of graphs for which this problem has been previously shown to have FPT algorithms and/or polynomial kernels. In particular, our result implies that the problem restricted to bounded- degenerate graphs has a polynomial kernel, solving an open problem posed by Alon and Gutner.