Rafael Nadal will be hoping he can avoid an upset at the US Open. Photo: Adam Hunger/AP Photo

NEW YORK  Three-time champion Rafael Nadal is the favourite on paper as an upset-filled US Open reaches the semi-final stage where the honour of the big three in men's tennis is also at stake.

Roger Federer, Novak Djokovic and Nadal are said trio which has dominated the game ever since Federer won his maiden Wimbledon title 16 years ago.

So stark has been their dominance that there have been only five of the 65 grand slam finals since that 2003 match in which none of the three has featured, the last being the 2016 Wimbledon final in which Andy Murray beat Milos Raonic.

With Djokovic retiring injured in the last 16 and Federer ousted in the quarter-finals, Nadal is the last one standing as he heads into Friday's semi against Italy's Matteo Berrettini, with in-form Daniil Medvedev and Grigor Dimitrov contesting the other match.

The second-seeded Nadal advanced into his 33rd semi at the majors and eighth at Flushing Meadows against Diego Schwartzman, wasting big leads in the first (4-0) and second (5-1) sets before succeeding in straight sets.

"I need to play my best, and today I think I make a step forward, even if I lost my serve a couple of times," Nadal said afterwards.

The winner of 18 grand slams will not underestimate the 23-year-old Berrettini who is in his first major semi after enjoying a splendid year with titles in Budapest and Stuttgart, two further finals and being the 24th seed in New York.

"Berrettini is having a great year. He's in semi-finals winning a lot of good matches. You can't expect an easy opponent. You can't expect an easy match," Nadal said.

Berrettini outlasted French 13th seed Gael Monfils in a fifth-set tiebreak but is also well aware of what he faces next.

"He's the greatest fighter ever in this sport," Berrettini said. "I admire him, the way he's on the court. His attitude is something that is close to perfection."

But he also insisted: "I'm in semis. I'm trying to keep going, and I'm dreaming as well. Why not?"

Medvedev has meanwhile confirmed his role as dangerous dark horse as he reached his first career semi at the majors in what could be the culmination of a strong North American summer swing that saw him lift the trophy in Cincinnati and reach the Washington and Montreal finals.

"That's what I've been working for all my life, especially the last two and a half years. That's where I've been going step by step. I was improving my rankings. But I am still really surprised with the way this last four weeks have been going," he said.

Medvedev had a strained relationship with the critical New York fans early on but that improved in his quarter-final win against 2016 champion Stan Wawrinka.

The 23-year-old is happy to have two days off to treat his various aches and pains from the heavy schedule and is taking nothing for granted against Dimitrov, saying: "We all know what he's capable of when he's playing like he can."

Dimitrov is in his third grand slam semi after upsetting Federer, the former world number three returning to form after two difficult and injury-marred years that have seen him slip to 78th in the rankings.

"I think the past six, seven months have been pretty rough for me. But I had somebody to lean on, my friends, my family," he said.

"Next thing you know, you're almost end of the year, you have a result like this. It's pretty special to me."

dpa