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Paul Antony Butler has pleaded guilty at Plymouth Crown Court to the murder of university lecturer Claire Chick.
Butler, 53, of Stangray Avenue, Plymouth, also admitted one charge of possession of a bladed article.
Ms Chick, 48, was found seriously injured in West Hoe Road just before 21:00 GMT on 22 January and later died in hospital.
Butler, who appeared at court via video link from prison, is due to be sentenced on 25 April.