Is the direction of the ticket important? Do cities have to be connected in the order shown on the ticket?
For example, if I am attempting to claim the Rostov-Erzurum ticket, can I connect Erzurum to Rostov instead of connecting Rostov to Erzurum?
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In both Ticket to Ride and Ticket to Ride: Europe, routes can be completed in any order, and there's no concept of direction of travel. All that matters is whether you can reach one of the cities from the other at the end of the game.
If, by the end of the game, a player has created a continuous path of his color plastic trains between the two cities named on a Destination Ticket he holds, he scores the additional points indicated by the Point Value on the Ticket. If he has failed to complete a continuous path between those cities, he deducts the Point Value on the Ticket from his total score.
A path between cities must be created. Nothing about traveling from one of the cities to the other city.
For example, you could satisfy a Rostov-Erzurum ticket by having built Erzurum-Sevastopol, Rostov-Sochi, and Sevastopol-Sochi in any order.
This is a related question about Train Stations in Ticket to Ride: Europe.