Murder victim Melanie Jayne Gray was found half-naked and may have been killed as she struggled with a sex attacker.
As relatives today paid tribute to their "loving" sister, police admitted robbery was not the motive - but sex may have been.
The 38-year-old victim, a mother of five, was repeatedly knifed before the killer torched the home where she lived with her partner.
Her boyfriend, of the same age, has been ruled out as a suspect - he was being questioned by police at the time of the murder in connection with an unrelated matter.
Police would not reveal details of the wounds Ms Gray suffered but sources told The Argus she had been repeatedly knifed and she was discovered naked from the waist down.
Detectives were hoping a mystery man seen near the murder scene in Three Bridges Road, Crawley, in the early hours of Sunday would provide them with vital clues.
He ran towards the nearby Plough pub between 11.30pm on Saturday and just after midnight, when firefighters arrived to tackle the blaze.
He is white and wore a short-sleeved shirt and dark trousers or jeans.
Ms Gray's sister Lilian Gunning, in a statement, appealed for help from witnesses.
She said: "Melanie was our wonderful, kind and loving sister as well as being a much-loved mother and daughter. She was above all our friend.
"We have many wonderful memories and have been hearing the same from so many people. It just seems unbelievable that she is no longer with us.
"Melanie had so many friends and we would like to thank all those who have managed to contact us for their sincere kindness and help but we would ask for a short time to ourselves to remember Melanie in our own way.
"I would ask everyone to help us. Anyone who has even the smallest shred of information please let the police know so Melanie can have peace."
Ms Gray, married three times and separated from her last husband, had five children, the oldest 21, who all live in Sussex. She worked for West Sussex County Council as a chaperone for children.
The shelter she was living at, for single parents and children, was not her home. She lived in Furness Green, Crawley but decided some months ago to move in with her partner.
Ms Gray had been with her partner for a year and his child also lived in the hostel.
Thirteen people fled the building and police said the arson attack could have taken more lives.
Detective Chief Inspector Adam Hibbert, heading Operation Edenberry, told a press conference yesterday: "This is a tragic event and we sympathise greatly with Melanie Gray's family.
"The person responsible attempted to set fire to the premises and in doing so risked the lives of many other people. The consequences could have been far more serious."
Detectives are still trying to piece together Ms Gray's last movements on the day she was killed.
Mr Hibbert said a murder weapon had not been found but confirmed police are looking for a knife.
Firefighters found her body lying in a pool of blood as they tackled the blaze in the early hours of Sunday morning.
A post mortem carried out the following day confirmed she had been stabbed.
Floral tributes to Ms Gray were laid outside the hostel by family members and friends.
Anyone with any information should contact Sussex Police on 0845 6070999 or Crimestoppers on 0800 555111.
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