Murder detectives investigating a deliberate blaze in Milngavie are hoping to trace a man in "army combat clothing" seen around the time of the fire.

Cameron Logan, 23, was murdered in the fire at his family home in the East Dunbartonshire town in the early hours of New Year's Day.

His girlfriend, 24-year-old Rebecca Williams, known as Bex, was injured in the blaze and remains in a critical condition in hospital.

On Friday, Police Scotland said they are looking to speak to a man seen walking on the West Highland Way around the time of the fatal fire.

The force said the man was wearing "army combat clothing" and is believed to routinely walk from Maryhill to the start of the trail in Craigton Road, often passing through Milngavie.

Detective chief inspector Paul Livingstone said the man "may also have information which may assist the ongoing inquiry."

"It remains a priority for officers to speak with these people to determine whether or not they have seen anything which may be of importance to the investigation," he said.

"We continue to seek information on the dark-coloured car that reportedly had its engine running at the lay-by on Craigton Road and we would continue to ask anyone with information to come forward.

"A family continues to grieve following the death of their son. A young girl remains in hospital, where medical staff describe her condition as critical but currently stable.

"We are doing all we can to trace the person responsible and to ensure that that they are held to account for their actions."

Previously, police had appealed to trace a motorist seen in Craigton Road close the blaze in Achray Place, while they also sought to track down dog walkers who had been in the area between 7.40am and 8.10am on January 1.

Mr Cameron's mother and father, both aged 54, suffered smoke inhalation in the blaze while the family's dog died in the incident.

Mr Livingstone said: "A number of local residents have now come forward with the belief that they may have been the dog walkers previously described.

"We do know that there were a number of individuals walking dogs around the time of the incident, so please continue to contact us if you believe you have information which may help our inquiry.

"I would continue to ask those who are yet to come forward to do so now. You may not think the information you have is relevant, or important, but as part of our ongoing investigation, the smallest detail could make all the difference to our investigation."

Ms Williams and Mr Logan had been celebrating on Hogmanay and walked home in the early hours of New Year's Day.

Detectives say the fire had been set deliberately, resulting in the death of psychology student Mr Logan.

Ms Williams, a broadcast journalist with Global Radio, was taken to the Queen Elizabeth University Hospital in Glasgow.

Earlier on Friday, her father Phillip Williams had stated in a Facebook post that she was "fighting hard" in hospital.

Anyone with information relating to the fire murder is asked to contact the police on 101.