Computing densest k-subgraph with structural parameters

Abstract

Densest k-Subgraph is the problem to find a vertex subset S of size k such that the number of edges in the subgraph induced by S is maximized. In this paper, we show that Densest k-Subgraph is fixed parameter tractable when parameterized by neighborhood diversity, block deletion number, distance-hereditary deletion number, and cograph deletion number, respectively. Furthermore, we give a 2-approximation \(2^{{{\texttt{tc}}(G)}/2}n^{O(1)}\)-time algorithm where \({{\texttt{tc}}(G)}\) is the twin cover number of an input graph G.