Another look at the degree constrained subgraph problem

There are several versions of the degree constrained subgraph problem. Earlier work used the linear programming approach to solve the problem. However, a more combinatorial approach is presented. A restricted problem is reduced to the regular maximum matching problem by means of a simple construction. The same construction yields a reduction of the weighted version of this problem to the weighted maximum matching problem. An alternating path technique is used to obtain a solution to the general problem from that of the restricted problem. The corresponding weighted problem is reduced to the weighted matching problem. An application is made to an edge-partitioning problem that is closely related to edge-coloring problems. Figures.