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A woman reported that she was assaulted in an alleyway and another reported a domestic incident last night.
Police were spotted in an alleyway near Freeman Road in Gravesend at 6.40pm after reports a woman was assaulted.
A 26-year-old man from Gravesend was arrested on suspicion of assault and remains in police custody.
A police helicopter was then seen flying over the Swanscombe and Greenhithe area just before 10pm.
Police cars and officers were also spotted on London Road in Greenhithe.
A police spokesman said: "It was assisting officers on the ground to look for a man following a domestic incident reported by a woman in Greenhithe."
A 21-year-old man was arrested and is being held on suspicion of criminal damage.