MELBOURNE:  Serena Williams and Novak Djokovic opened their title defenses with straight-set wins at the Australian Open in back-to-back matches on Rod Laver Arena.

The most dominant players in tennis entered the season's first major after contrasting preparations, with Williams having to overcome a left knee problem that limited her court time and Djokovic warming up with a run to the title at Doha.

Williams made a bright start, in a way, holding up one finger and twirling in her neon yellow two-piece outfit to celebrate her 6-4, 7-5 over Camila Giorgi on Monday. Djokovic had a 6-3, 6-2, 6-4 win over Chung Hyeon of South Korea.

Williams and Djokovic each won three of the four major titles last season, with Williams falling two matches short of a calendar-year Grand Slam when she lost in the U.S. Open semifinals and Djokovic's only loss coming in the French Open final.

Yet she dropped just one service game against No. 34-ranked Giorgi, who struggled with 12 double-faults, including one on the decisive break point in the 11th game of the second set.

Williams fired two aces and a service winner in the last game.

"I haven't played a competitive match in a really long time, but I think it was really good for me to come out here," Williams said. "I was able to stay in it and stay calm today and I think that's what matters most."

Williams said she needed the break to recharge at the end of last season and felt OK about her limited preparation.

"I haven't played in a long time, but I have been playing for 30 years, so it's kind of -- I try to focus on that," she said.

Two-time Wimbledon champion Petra Kvitova earned the distinction of winning the first completed match at the tournament when she beat Thai qualifier Luksika Kumkhum, avenging her upset three-set loss in the first round here in 2014.

Kvitova, who had to withdraw from a warmup tournament in China because of a stomach virus, said her preparation was disrupted and she was nervous ahead of the rematch with Kumkhum.

"Now I can breathe a little bit normally," she said. "I got really nervous before the match. I didn't sleep well actually. The memories from two years ago were a little bit difficult."

No. 24 Sloane Stephens, who beat Serena Williams in the 2013 Australian Open quarterfinals, lost 6-3, 6-3 to Chinese qualifier Wang Qiang, while No. 26 Anastasia Pavlyuchenkova and No. 27 Anna Karolina Schmiedlova also went out in the first round.

Djokovic's bid for a sixth Australian Open title started in temperatures of 34 Celsius (93 Fahrenheit), and he became annoyed with himself and his play at times, including three double-faults.

Overall, though, he was consistently too good for one of the up-and-coming players on tour. He said everything started looking up for him when he became a dad back in 2014, then joked about maybe having another baby.

Sixth-seeded Tomas Berdych, a semifinalist last year, opened his 50th consecutive major by beating Yuki Bhambri of India 7-5, 6-1, 6-2, and No. 7 Kei Nishikori had a 6-4, 6-3, 6-3 win over Philipp Kohlschreiber.

Also advancing were No. 12 Marin Cilic, No. 15 David Goffin, No. 19. Dominic Thiem and No. 26 Guillermo Garcia-Lopez. No. 22 Ivo Karlovic was the first of the men's seeds to exit the tournament when he retired due to a left knee injury while trailing Federico Delbonis 7-6 (4), 6-4, 2-1.

The hours before the tournament began were overshadowed by news reports alleging match fixing that had gone unchecked.

The ATP, which runs the men's tour, and Nigel Willerton, head of the Tennis Integrity Unit, represented the four governing bodies of tennis — the ATP, the WTA, the Grand Slam Board and the International Tennis Federation — in a joint news conference to reject the allegations published by the BBC and BuzzFeed News.

The reports, citing secret files, said that in the last decade 16 players — all at some stage ranked in the top 50 — have been repeatedly flagged to the integrity unit.

ATP chairman Chris Kermode said tennis authorities "absolutely reject any suggestion that evidence of match-fixing has been suppressed for any reason, or isn't being investigated."

Tennis Integrity Unit investigations have resulted in 18 successful disciplinary cases, including five players and one official who have been banned from the sport for life.