On the approximability of some degree-constrained subgraph problems

In this article we provide hardness results and approximation algorithms for the following three natural degree-constrained subgraph problems, which take as input an undirected graph G = (V, E). Let d >= 2 be a fixed integer. The MAXIMUM d - DEGREE-BOUNDED CONNECTED SUBGRAPH (MDBCSd) problem takes as additional input a weight function omega : E -> R+, and asks for a subset E' subset of E such that the subgraph induced by E' is connected, has maximum degree at most d, and Sigma(e is an element of E') omega(e) is maximized. The MINIMUM SUBGRAPH OF MINIMUM DEGREE >= d (MSMDd) problem involves finding a smallest subgraph of G with minimum degree at least d. Finally, the DUAL DEGREE-DENSE k-SUBGRAPH (DDDkS) problem consists in finding a subgraph H of G such that vertical bar V(H)vertical bar <= k and the minimum degree in H is maximized. (C) 2012 Elsevier B.V. All rights reserved.