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Celtic took full advantage of Hearts' slip at Hamilton to go top of the Premiership, while Aberdeen, Ross County and Motherwell all won.
Premiership Dundee, Hamilton and Partick were all dumped out of the Scottish League Cup at the second round stage.
Ronny Deila expects Virgil van Dijk to remain at Celtic, even if the club fail to qualify for the Champions League.
Hearts maintained their 100% Scottish Premiership record on Saturday, with Celtic, St Johnstone, Ross County, Hamilton and Aberdeen also winning.
Kilmarnock twice came from behind to earn a 2-2 draw against Celtic in the Scottish Premiership at Rugby Park on Wednesday evening.