An example of such a reduction would be the L-reduction.

A pair of functions f and g is an L-reduction if all of the following conditions are met:

L-reduction ("linear reduction") is a transformation of optimization problems which linearly preserves approximability features.

The problem is APX-complete, which directly follows from the APX-completeness of the vertex cover problem, and the existence of an approximation preserving L-reduction from the vertex cover problem to it.