Finding Connected Dense k-Subgraphs

Given a connected graph G on n vertices and a positive integer k <= n, a subgraph of G on k vertices is called a k-subgraph in G. We design combinatorial approximation algorithms for finding a connected k-subgraph in G such that its density is at least a factor Omega(max{n(-2/5), k(2)/n(2)}) of the density of the densest k-subgraph in G (which is not necessarily connected). These particularly provide the first non-trivial approximations for the densest connected k-subgraph problem on general graphs.