  In the present paper we consider the problem of constructing all the
projective rooted spanning trees of a given graph. We propose an algorithm
based on reducing this problem to the problem of constructing all the maximal
independent sets of a certain derived graph. We also offer an algorithm for
step-by-step growing the spanning trees that sifts, at each step, any sub-trees
non-extendable to projective spanning trees. The proposed algorithms were
applied for analyzing the possible variants of the syntactic subordination of
nouns through prepositions .
