The problem of existence of a tree satisfying a given set of constraints on its vertices is considered. Specifically, given finite set of constraints P = {p1, p2, ..., pn}, we ask if there is an efficient algorithm to build a line-tree T = (V, E) such that for every constraint pi = (ab)(cd), where a, b, c, d are arbitrary elements of V , the path (ab) does not share any vertices with the path (...