Constructing the highest degree subgraph for dense graphs is in N b A S

AbstractIn this paper, we first show that the Highest Degree Subgraph problem remains P-complete for dense graphs (i.e. when m = Ω(n2poly log n)). This hardness result gives a clear motivation in studying the approximability of the Highest Degree Problem even for this restricted case. We then provide an N b-approximation scheme computing approximate solutions for dense graphs, thus proving that, in this case, the problem belongs to the N b A S class