  In this work, I present an optimization problem which consists of assigning
entries of a stellar catalog to multiple entries of another stellar catalog
such that the probability of such assignment is maximum. I show a way of
modeling it as a Maximum Weighted Stable Set Problem which is further used to
solve a real astronomical instance and I partially characterize the forbidden
subgraphs of the resulting family of graphs given by that reduction. Finally, I
prove that the problem is NP-Hard.
