Carlos Alcaraz marked his return to the Australian Open in convincing fashion with victory over veteran Richard Gasquet.

Alcaraz missed the tournament last year with a leg injury and was in a hurry to make it through to round two, clinching a 7-6 (5) 6-1 6-2 win under the lights on Rod Laver Arena.

Gasquet, 37, stood toe to toe with Alcaraz in the opening set and hit the shot of the match with a signature one-handed backhand down the line in the tie-break.

But, once Alcaraz had come through that, he ran away with the contest, losing only three more games.

Sixth seed Alexander Zverev had to come from a set down to see off German compatriot Dominik Koepfer 4-6 6-3 7-6 (3) 6-3, but the focus in the press room was on his forthcoming court date.

It was announced on Monday that Zverev will face a trial starting in May over domestic abuse allegations made by a former girlfriend.

Zverev, who denies the charges, was given a penalty order and fined in November but opted to contest that at a hearing.

He had previously been accused of abuse by another former girlfriend, who did not pursue legal action, which he also denied.

Asked whether it is appropriate for him to be on the ATP Council, which represents players, Zverev said: “Why would it not be? Nobody has said anything to me. I don’t have a reason not to believe that.”

Several of the German’s fellow players declined to give an opinion on the same question in their press conferences, but women’s world number one Iga Swiatek said: “For sure it’s not good when a player who’s facing charges like that is kind of being promoted.”

Zverev was then pushed on whether he should be allowed to play on the tour while the case is pending, with the 26-year-old responding: “Journalists are saying that. Some who are actually interested more in this story to write about and more about the clicks than the actual truth.”

It was a good day on court for the leading names, with eighth seed Holger Rune defeating Yoshihito Nishioka 6-2 4-6 7-6 (3) 6-4 while 11th seed Casper Ruud eased to a 6-1 6-3 6-1 win over Albert Ramos-Vinolas.

Grigor Dimitrov, the 13th seed who won the warm-up tournament in Brisbane, had to come from a set and a break down to defeat Marton Fucsovics in four.