The Minimal Cut Cover of a Graph

We consider a problem which occurs in testing for short circuits in printed circuit board components. This problem can be modeled as the covering of the edges of an undirected graph by cuts. In particular, we look for a family of cuts F = f(C1; C1) : : : ; (C; C)g with minimal cardi-nality , such that each edge belongs to at least one (Ci; Ci). We call this problem the Minimal Cut Cover problem, MCC for short. For the special case of complete graphs, Loulou 7] describes a polynomial greedy-like method for MCC. Here we will show that MCC is NP-hard for arbitrary graphs, by drawing the relationship to the vertex color problem. Furthermore we give some algorithmic approaches for solving MCC approximately.