Falkirk manager Peter Houston is leaving his post with "immediate effect" following the club's poor start to the season.
Dundee United went top of the Championship with a 2-1 win over Queen of the South secured through Scott Fraser's second-half goal.
Paul McMullan gave Dundee United victory at Inverness CT on the opening day of the Scottish Championship season.
The pressure on Hearts coach Ian Cathro has been cranked up after they were dumped out of the League Cup by Dunfermline.
Dundee and Dundee United will face each other again in the Betfred Cup after being paired together at Dens Park.
Peterhead stunned Hearts 2-1 in the Betfred Cup group stage on Tuesday, while Albion Rovers beat Hamilton on penalties.
Kyle Lafferty continued his bright start to life at Tynecastle with a well-taken double against East Fife in the Betfred Cup.
Dundee United came from behind to beat Falkirk and reach the Scottish Premiership play-off final.
Motherwell secured their Premiership survival at the expense of Hamilton on the back of a 3-1 win over Kilmarnock.
St Mirren have retained their Ladbrokes Championship status after getting the point they needed at champions Hibernian.
St Mirren boosted their Scottish Championship survival hopes with an emphatic 5-0 victory over fellow strugglers Raith Rovers at Paisley 2021 Stadium.
Falkirk's Myles Hippolyte has accepted a two-game ban for simulation after his somersault dive to win a penalty against Dunfermline.
Falkirk maintained their hold on second place in the Scottish Championship as they fought back from a goal down to defeat 10-man Dunfermline.
Hibernian clinched the Scottish Championship title with an emphatic 3-0 victory at home to Queen of the South.
Hibernian remain nine points clear at the top of the Scottish Championship after a 1-1 draw with Greenock Morton.
James Keatings scored a stoppage-time winner as Hibernian beat Falkirk 2-1 in the Scottish Championship at Easter Road.
There are still nearly two months of the season remaining, but promotion and relegation could be decided this weekend.
Hibernian beat 10-man Ayr Utd 3-1 to reach the Scottish Cup semis, while Dunfermline and Falkirk both recorded Championship wins.
Aberdeen tightened their grip on second spot in the Scottish Premiership with a 1-0 win over Ross County at Pittodrie.
Hibernian moved seven points clear at the top of the Championship after drawing 1-1 with Raith Rovers in Kirkcaldy.
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