def in_general_position(G, u, v, w):
    def on_path(x, y, z):
        d = None
        for p in G.shortest_simple_paths(y, z):
            if d is None:
                d = len(p)
            elif len(p) > d:
                return False
            if x in p:
                return True
        return False

    return not (on_path(u, v, w) or on_path(v, u, w) or on_path(w, u, v))

@cached_function
def statistic(G, value_only=True):
    V = frozenset(G.vertices())
    def children(M):
        for u in V.difference(M):
            if all(in_general_position(G, u, v, w) for v, w in Subsets(M, 2)):
                yield M.union([u])

    R = RecursivelyEnumeratedSet([frozenset()]
                                 + [frozenset([u]) for u in V]
                                 + [frozenset(uv) for uv in Subsets(V, 2)], children)
    if value_only:
        return max(len(M) for M in R)
    return R