Removing the condition of visiting each city "only once" does not remove the NP-hardness, since it is easily seen that in the planar case there is an optimal tour that visits each city only once (otherwise, by the triangle inequality, a shortcut that skips a repeated visit would not increase the tour length).
Uklanjanje stanje poseti svaki grad "samo jednom" ne ukloni NP-tvrdoće, jer se lako može videti da je u planarna slučaju postoji optimalan turneje koja posećuje svaki grad samo jednom (inače, po trougao nejednakost, prečica koja preskače ponavljanjem posetu ne bi povećanje dužine turneje).