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• Djokovic recovers from slow start to move past Michelsen on Shanghai return

  Novak Djokovic marked his Shanghai Masters return with a hard-fought straight-sets win over Alex Michelsen.

  The four-time champion, who is appearing in this event for the first time since 2019, required two tie-breaks before prevailing 7-6 (7-3) 7-6 (11-9) in just under two hours.

  Djokovic, still donning a protective sleeve over his right knee, made a slow start in only his second match since losing to Alexei Popyrin in the US Open third round, winning just four points in the first three games as he fell 4-1 behind.

  However, the 24-time major winner broke back in the seventh game before dominating the tie-break for first blood.

  Roles were reversed in the second set as Michelsen cancelled out an earlier break in game seven.

  However, the American squandered two set points to level and was eventually punished by Djokovic, who will play either 28th seed Flavio Cobolli or three-time major winner Stan Wawrinka in the next round.

  Data Debrief: Djokovic continues American dominance

  Djokovic was given an early scare, but his experience eventually showed as he came through.

  Including team events, the Serb has now won his last 33 ATP-level matches against American opponents, with his last such defeat coming against Sam Querrey at Wimbledon in 2016. 

  The 24-time major winner also demonstrated his determination when the pressure intensified, and he has now come through 12 of his 16 tie-breaks played this season.

• Gauff fights back to beat Badosa in China Open semi-finals

  Coco Gauff recovered from a set and a break down to reach the China Open final with a 4-6 6-4 6-2 victory over Paula Badosa on Saturday.

  Having given up an early break in the opener, Gauff got one of her own by converting her eighth break point in a mammoth eighth game featuring 10 deuces, only for Badosa to hit back immediately to go a set up.

  Gauff lost serve immediately in the second set to go on the back foot, only to level the match with back-to-back breaks, the second of them to love.

  The decider began with a series of breaks, Gauff taking two of them as the momentum swung her way, then she protected her lead all the way to reach her first final since winning January's Auckland Open.

  The 20-year-old is the youngest player to reach the women's singles final at the China Open since Caroline Wozniacki in 2010.

  She has fought from a set down to win in each of her last three matches, the first time she has done so in her career. She is the first player to do so in WTA-1000 events since Iga Swiatek at Indian Wells 2022.

  Data Debrief: Gauff brings up century

  Saturday's match was Gauff's 100th at WTA 1000-level events, and her 67th such victory.

  Among American players, only Serena Williams (87), Venus Williams and Jessica Pegula (70) have bettered her 67 wins through their first 100 matches at such events.

• Alcaraz beats home favourite Shang in Shanghai opener

  Carlos Alcaraz began his Shanghai Open campaign with a straight-sets win over China's Shang Juncheng, bringing up his 10th straight victory.

  Just three days on from his epic victory over Jannik Sinner in the China Open final, Alcaraz recorded a 6-2 6-2 win over Shang inside one hour and 17 minutes.

  The four-time grand slam winner wasted no time by breaking in the very first game of the encounter, then repeated the trick six games later to take the opener, avoiding any pressure as he won 82% of his first-serve points.

  Alcaraz produced the shot of the match early in the second set, producing a brilliant backhand flick to salvage a point while backtracking from the net.

  Back-to-back breaks midway through the second set sealed Alcaraz's 10th straight victory, after which he hailed the performance of his 19-year-old opponent.

  "I'm not used to playing against players younger than me," Alcaraz said. "He has been playing good tennis lately, winning his first ATP title [in Chengdu], so I'm pretty sure he's going to climb the rankings. 

  "At the net he told me that it's a pleasure share the court with you. So these kinds of things that I hear from younger players, it's great."

  Data Debrief: Double figures for Alcaraz

  Alcaraz's victory was his 10th in succession since he suffered a shock second-round defeat to Botic van de Zandschulp at the US Open in August.

  He will face another Chinese player in the next round, taking on world number 560 Wu Yibing.