On some network design problems with degree constraints

► For the problem of finding a 2-connected subgraph with degree bounds we give a bicriteria constant approximation. ► We give an O˜(k/opt) approximation for finding a directed k-tree with minimum outdegree. ► We give a constant ratio for the prize collecting version of the second problem. ► For Steiner forest with hard degree bounds of 1, we give an O(log3n) ratio.