Roger Federer marked his return to Roland Garros with a straight-set defeat of Uzbekistan qualifier Denis Istomin on Monday.
The 39-year-old Federer, the champion in Paris in 2009 but playing the event for only the second time since 2015, won 6-2, 6-4, 6-3.
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Medvedev also triumphed 6-3, 6-3, 7-5 as he looks to take advantage of being in the opposite part of the draw from Novak Djokovic, Rafael Nadal and Roger Federer.
Italian prospect Jannik Sinner saved a match point as he laboured to a 6-1 4-6 6-7(4) 7-5 6-4 victory against France’s Pierre-Hugues Herbert in the first round.