Figures (i) and (ii) below represent intercity highway systems, where each black dot is a city and each line segment joining two dots is a direct highway between those two cities. Figure (i) is a 4 by 4 grid of cities connected only along the horizontal and vertical grid lines, with no diagonal roads. Figure (ii) has 5 cities joined by 6 highways in an irregular network with one extra interior city.
A salesperson needs to make a trip. She needs to start from a city, visit each of the remaining cities exactly once, and finally return to the same city from which she started. Which one of the following options is then true?