The Maximum Degree-and-Diameter-Bounded Subgraph Problem

Introduction
Given a connected host graph G, an upper bound for the degree d, and an upper bound for the diameter k, we look for the largest subgraph S of G with maximum degree at most d and diameter at most k. This problem contains  the Degree-Diameter Problem as a special case (namely, by taking a sufficiently large complete graph as a host graph). The problem was defined in (Dekker et al, 2011), where some applications were discussed, and a polynomial-time approximation algorithm was proposed. Regarding its computational complexity, the problem is NP-hard, and not in APX (i.e. it cannot be approximated to within a constant factor in polynomial time).

MaxDDBS in special classes of host networks
MaxDDBS in the mesh

MaxDDBS in the honeycomb

MaxDDBS in the hypercube