Trav and Kourt were exploring the sites in Portofino as they walked hand in hand. They were both covered in large, almost-matching hoodies as they traversed the town.

This has been a super-romantic vacay for the 2 ... they've been exploring Italy in what is clearly a budding relationship. In fact, scratch budding ... it's full-blown at this point.

It's a huge moment for Travis, who just recently started flying again. As you know, he hasn't gotten on an airplane since the fatal crash 13 years ago that killed 4, including 2 of his close friends.

He flew for the first time a few weeks back when he, along with Kourtney, Kris Jenner and Corey Gamble, took Kylie's jet down to Cabo in Mexico.

The Cabo trip removed any doubt they are in a downright serious relationship ... making out in the main pool for all to see. The experience onboard a plane seemed tolerable enough for Travis to do it again.