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Police will monitor social media and deploy extra officers in and around Glasgow as Celtic and Rangers meet for the first time in almost three years this weekend.
The League Cup semi-final match at Hampden on Sunday is a sell-out and police said they will target anyone planning to cause trouble.
Tensions are set to be high in what is the first game between the clubs since Rangers' liquidation in 2012.
Yesterday, Celtic manager Ronny Delia revealed that both clubs have been visited by officers to remind players and management of their responsibilities in a bid to minimise any possibility of trouble.
The match is being broadcast live on BBC Scotland but some pubs in Glasgow have said they will not be showing it.
Aberdeen and Dundee United will also play at Hampden on Saturday in the other semi-final.
Chief Superintendent Andy Bates, the match commander for the weekend, said the force is "well-versed in policing high-profile matches''.
"These are significant semi-final matches for all the teams and supporters involved,'' he said.
"Once again, Glasgow will be the focus of attention with a large number of visitors expected in the city.
"We're well-versed in policing high-profile matches and sporting events, and we have an appropriate plan in place to ensure the safety of people attending the matches and visiting the city.
"These two semi-finals bring together four teams that are great rivals and I am sure that most supporters will enjoy the sporting occasion, however a minority may choose to cause disorder and my message to them is clear: anyone involved in disorder will be arrested.''
Officers are to be deployed at the stadium, in Glasgow city centre and at major transport hubs before, during and after the matches.
Those planning on drinking before the matches have been urged to do so responsibly.
Mr Bates said: "It is an offence to enter or even attempt to enter the stadium whilst drunk and both police and stewards will be looking out for anyone who is drunk or intent on causing disruption.''
Teams will also be monitoring online activity during the matches for offensive comments.
"In 2013/14 nine people were convicted of various football-related online offences, with one person being sent to prison for 12 months for a racial breach of the peace and drug offences after making an offensive comment about footballers,'' the match commander said.
"So far, in 2014/15, four people have also been reported to the procurator fiscal for a number of religious and racial offences.''
He added: "We had a superb year policing major sporting events in 2014 and the semi-final weekend provides yet another opportunity to showcase Glasgow on the world stage.
"Together we can make sure that football is the story in Monday's newspapers, not the behaviour of a minority of so-called fans.''