(CNN) - During Serena Williams' first-round, straight-sets win over Germany's Tatjana Maria at the Australian Open, one question kept surfacing: How would you describe her green, one-piece Nike outfit?
Was it a onesie? A leotard?
Williams set the record straight after her convincing 6-0 6-2 victory. "It's a Serena-tard," Williams said in her post-match press conference, drawing laughter from journalists.
World No. 1 Simona Halep was sure to be in good spirits after gaining revenge over Kaia Kanepi, while the ever watchable Nick Kyrgios fell in straight sets at home to 2016 Wimbledon finalist Milos Raonic.
Not so much of a light-hearted matter for Williams is why she continues to sport compression stockings.
The American revealed she almost died after giving birth to daughter Alexis Olympia in September 2017 due to a pulmonary embolism, a condition she had previously suffered from.
"Definitely still concerned," said Williams. "I have had some issues, and they're not done. So it's just something I just have to do for pretty much probably the rest of my career, we'll see. But I'm always at the doctor.
"With DVTs, it's very scary," she said, referring to the condition, deep vein thrombosis. "A lot of people have them. Especially for me it's incredibly frightening.
"I lay on the side of precaution as opposed to not."
The last time Williams played at the Australian Open, two years ago, she tallied a 23rd major while eight weeks pregnant.
Her performance Tuesday at Rod Laver Arena -- scene of her triumph against older sister Venus in 2017 -- suggests Williams will take some stopping at her joint-most successful grand slam, and the opening fixture win against Maria tees up an intriguing contest against a rejuvenated Eugenie Bouchard.
Williams owns seven majors from Melbourne, equaling her tally at Wimbledon.
Ominously for the rest of the field, six of those Australian Open titles have come in odd-numbered years, the exception being 2010.
There surely will be stiffer tests for Williams in Melbourne but her ball-striking and intensity might have made fans forget this is only the fourth grand slam of the 37-year-old's comeback -- the first set lasted just 18 minutes.
And there were no issues with chair umpire Zhang Juan, four months after clashing with Carlos Ramos in the US Open final, her last official outing. Beaten by Japan's Naomi Osaka in New York, Williams was then deprived of what would have been a record-tying 24th major.
Emotions running high
Such was the lopsided nature that the 74th-ranked Maria -- Williams' friend and neighbor in Florida, who also suffered from a life-threatening pulmonary embolism in 2008 -- was reduced to tears at the net when it ended.
It has been that kind of tournament so far. Britain's Harriet Dart wept after a 6-0 6-0 loss to her idol Maria Sharapova on Rod Laver Arena Monday, while emotions ran high in what might have been Andy Murray's final match.
Williams didn't want to linger in her press conference, keen on getting home to her daughter.
She, and her husband, Reddit co-founder Alexis Ohanian, have posted pictures on social media of Alexis' doll, Qai Qai, and Williams said giving her daughter a black doll was something she wanted.
"Growing up, I didn't have that many opportunities to have black dolls," said Williams. "And I was just thinking, like, I want her first doll to be black.
"And her heritage, obviously she's mixed, she's Caucasian and black, but I feel like that was her first doll and I said her second doll would be Caucasian," added Williams.
"I definitely want to always teach her love and teach her ... that humans should always have love for each other, no matter what color they are."
Kanepi crushed Halep in the first round of the US Open in August and when the huge-hitting Estonian took the first set in a tiebreak on Margaret Court Arena, lightning was about to strike twice. But the Romanian this time didn't succumb and earned a morale boosting 6-7 (2-7) 6-4 6-2 win.
Kanepi -- out of action with an injury since September -- suffered from a hand blister late in the final set.
Troubled by a bad back, Halep hadn't won a match since August and split with coach Darren Cahill in the off-season after the Australian said he wanted to spend more time with his family. The two remain friends and Cahill has even been on the practice court with the 27-year-old in Melbourne.
Kyrgios' Australian Open preparations were hampered when he was bit by a spider in the off-season. Raonic spun a service web over the Australian, hitting 30 aces and surrendering only 11 points on serve in a 6-4 7-6 (7-5) 6-4 triumph.
Having sustained his first reverse in the opening round at the Australian Open, Kyrgios' ranking is set to drop to 67th.
The often injured Kyrgios, seen by the trainer for a lingering knee injury, hit a shot between the legs and one behind his back in the seventh game of the second set. He lost both points. The much more focused Raonic -- who battles three-time grand slam winner Stan Wawrinka next -- was laser sharp.
Venus Williams, her ranking down to 36th after not reaching the second week of a major in 2018, rallied to beat 25th seed Mihaela Buzarnescu 6-7 (3-7) 7-6 (7-3) 6-2 to move one step closer to facing Serena in the fourth round. The 38-year-old trailed by a set and 5-3 before staging a comeback.
Her next challenger is France's Alize Cornet, one of the rare players on the tour to have beaten both sisters.
Like Serena Williams, men's No. 1 Novak Djokovic cruised -- once he overturned an early break deficit -- against US qualifier Mitchell Krueger, 6-3 6-2 6-2.
Djokovic is seeking a record seventh title at Melbourne Park but first since 2016. The man who upset the Serb last year, Hyeon Chung, struggled with a foot injury after his breakthrough 2018 event but the South Korean pulled off a stunning comeback to oust American Bradley Klahn 6-7 (5-7) 6-7 (5-7) 6-3 6-2 6-4 in 3 1/2 hours.
Luck for Japanese player
The luckiest tennis player this month in Australia? That could be Japan's Taro Daniel.
Daniel got into tournaments in Brisbane and Sydney as a lucky loser -- replacing high seeds, he earned a bye into the second round, too -- and advanced in Melbourne when Australian qualifier Thanasi Kokkinakis was forced to retire with a chest injury in the second set.
Kokkinakis had won the first, 7-5.
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