• p. 1681, Proposition 7:
  Proposition 7 is incorrect; a correct upper bound is 2^{2k}. The fact that "every crossing is encoded by two bits of different values" is not sufficient to conclude that there are at most 2^k different sequences encoding an arrangement. Moreover, it is not true that "We can also suppose that all the pseudochords crossing p_i start in the arc A_{a_i}", since we cannot easily identify the other bit corresponding to a crossing of p_j with p_i.
  A correct form of Proposition 7 is proved in the "sequel", [Improved enumeration of simple topological graphs, Discrete and Computational Geometry 50 (2013), Issue 3, 727-770, Proposition 21.]