A post-mortem into the marine biology student's death has not yet been completed, but Humberside police have revealed the foundation course student was assaulted prior to her killing.
Last night a 32-year-old man arrested in connection with her death was released with no police action but a 20-year-old man remains in custody.
He is currently being questioned but must be released at 15:00 BST this afternoon if police do not obtain authority to detain him for longer from magistrates.
Detective Chief Inspector Tony Garton appealed to members of the public and the student community to locate Ms Love's silver-coloured Nokia mobile phone.
"The phone may be of significance to the investigation but despite detailed searches of Rebecca's room… [it] has not yet been found," he said.
"We have a large team of experienced and dedicated officers and police staff who are sifting through the information and are following up several lines of enquiry."
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