Spain's Carlos Alcaraz Garfia (right) shakes hands with Denmark's Holger Rune (left) after giving up at the end of their men's singles quarter-final tennis match on day 5 of the ATP World Tour Masters 1000 - Paris Masters (Paris Bercy) - indoor tennis tournament at The AccorHotels Arena in Paris on Nov 4, 2022. (CHRISTOPHE ARCHAMBAULT / AFP)

World number one Carlos Alcaraz retired injured against Holger Rune at the Paris Masters on Friday, sending his fellow 19-year-old through to the semi-finals, while Novak Djokovic and Felix Auger-Aliassime also sealed their places in the last four.

Rune outclassed Alcaraz to win the opening set 6-3 and held firm in the second when the top seed raised his game before the Spaniard retired at 3-1 down in the tiebreak having received medical treatment for an abdominal strain at 6-5.

Carlos Alcaraz was hopeful of making a full recovery for his debut at the ATP Finals in Turin, which begin on Nov 13, despite the quick turnaround

"I cannot stretch. I couldn't serve well, I couldn't hit the forehand well said Alcaraz. "I preferred to retire and see it and take care of it."

Alcaraz was hopeful of making a full recovery for his debut at the ATP Finals in Turin, which begin on Nov 13, despite the quick turnaround.

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"I have some tests on how it's going to be before Turin," he added. "But right now I'm focused on trying to get better in the abdominal and trying to be at 100 percent in Turin."

Holder and sixth seed Djokovic made light work of Italian youngster Lorenzo Musetti in a 6-0 6-3 win and will next meet Greek fifth seed Stefanos Tsitsipas, who cruised past American Tommy Paul 6-2 6-4 in about 77 minutes.

A six-times winner in Paris, Djokovic served Musetti a 24-minute bagel and dropped only eight points in the first set before overcoming a brief wobble in the second, when he went a break down, to ease to victory.

Danish teenager Rune, bidding to reach four finals in a row, advanced to his first ATP Masters 1000 semi-final and earned his third top 10 win in as many days after seeing off Hubert Hurkacz and Andrey Rublev.

Spain's Carlos Alcaraz Garfia (center) receives medical treatment during the men's singles quarter-final tennis match between Spain's Carlos Alcaraz Garfia and Denmark's Holger Rune on day 5 of the ATP World Tour Masters 1000 - Paris Masters (Paris Bercy) - indoor tennis tournament at The AccorHotels Arena in Paris on Nov 4, 2022. (CHRISTOPHE ARCHAMBAULT / AFP)

He will take on eighth seed Auger-Aliassime in a battle between two of the Tour's most in-form players and a rematch of the Swiss Indoors final in Basel five days ago, which the Canadian won in straight sets.

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Auger-Aliassime extended his winning run to 16 matches after racing to a 6-1 6-4 win over Frances Tiafoe to remain on track for a fourth ATP title in as many weeks, having also won in Florence and Antwerp during his unbeaten run.

The 22-year-old cruised through the first set but Tiafoe dug deep to hold serve and save five match points before Auger-Aliassime sealed a 93-minute victory on his sixth attempt.

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"I feel better and better," Auger-Aliassime said. "Of course right now I'm playing well and feeling good, but I see things that I can still do better and still improve on to be able to top the game."