In this paper, we introduce a new problem related to bipartite graphs called
minimum maximal k-partial-matching (MMKPM) which has been modelled by
using a relaxation of the concept of matching in a graph. The MMKPM problem can
be viewed as a generalization of the classical Hitting Set and Set Cover
problems. This property has been used to prove that the MMKPM problem is NPComplete.
An integer linear programming formulation and a greedy algorithm have
been proposed. The problem can be applied to the design process of finite state
machines with input multiplexing for simplifying the complexity of multiplexers
