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Carlo Dawes, 34, of Taunton Road, Bevendean who has been charged with the murder of Graham Pethard, 37, from Liverpool, was remanded back into custody following his appearance at Brighton Magistrates' Court on Monday morning.
Dawes is due to appear before Lewes Crown Court on Wednesday 9 May for a committal hearing.
Detective Inspector Phil Mays who is leading the investigation said: "This has been a fast paced investigation and I'm grateful for the support we have had from the people of Bevendean, who have no doubt experienced some disruption to their daily lives over the last few days.
"A further search of the crime scene is taking place this morning (7 May) and then we intend to remove the police cordon around the property on Taunton Road this afternoon.
"A knife was recovered yesterday (6 May) not far from the scene and will be forensically examined in due course.
"High visibility patrols will remain in and around the Bevendean area over the coming days and again I would like to appeal again to anyone who has information that could assist the investigation and has not yet come forward, to please call 101 quoting Op Abinger or call Crimestoppers anonymously on 0800 555 111."
Speaking from their home in Liverpool the family of Graham Pethard, (pictured) said: "Graham was a loving father who idolised his children. He was also a father figure to his friends and all who ever knew him.
"He was the sort of man who would be there before anyone and for anyone.
"He will be sadly missed by all who knew him, especially his four lovely daughters."