A 20-year-old man has been arrested over the brutal, opportunistic killing of Israeli student Aiia Maasarwe in Melbourne's north.
It is understood the young man was identified as a key person of interest after forensic tests were conducted on clothing dumped not far from the scene.
"The 20-year-old was arrested in Greensborough by local police working in partnership with homicide detectives about 11.20am," police said in a statement.
"Homicide squad detectives have arrested a man as part of the ongoing investigation into the death of Aiia Maasarwe."
The alleged killer has been described by police as an "opportunistic" attacker, whose random crime was "absolutely horrific".
It is believed he may have been left bloodied after the attack and also took several items from Ms Maasarwe's handbag.
A distinctive black cap with the number "1986" and a two-tone grey Cotton On T-shirt, which police strongly suspect were dumped by the alleged killer after the attack, have been crucial to the investigation.
The cap and T-shirt were found by police less than 100 metres from Ms Maasarwe's body.
"Someone in the community knows about this. Someone has gone home on Tuesday night, or in the early hours of Wednesday morning, maybe with blood on them, missing items of clothing. Somebody knows about this," homicide squad Detective Inspector Andrew Stamper said on Thursday.
"Nothing in the victim's background indicates this was anyone known to her. So yes, unfortunately, the presumption at this stage is this was a random and opportunistic attack."
Inspector Stamper would not say whether a weapon had been used in the murder, or detail the injuries to Ms Maasarwe's body out of respect for her family.
The scene has been described by police sources as being "horrendous as you could get".
Ms Maasarwe was on her way home from a gig at The Comics Lounge in North Melbourne and was speaking to her sister on the phone via FaceTime when she was attacked.
On Tuesday night, she was with new friends at Flagstaff Gardens in the CBD to practise her English, before going to a gig at The Comics Lounge in North Melbourne.
Ms Maasarwe was driven by friends from the comedy club to the CBD, where she caught the Route 86 tram from Bourke Street about 10.50pm.
Detectives have released CCTV images of the young student leaving the comedy club late in the evening.
She got off the tram at the Plenty Road stop near Main Drive, Bundoora, about 12.10am.
It is the tram stop closest to her student accommodation near La Trobe University in Bundoora, in Melbourne's north.
Ms Maasarwe was found unresponsive by window washers in a grass area outside Polaris shopping centre, 100 metres from the tram stop, on Main Drive, about 7am on Wednesday.
Inspector Stamper said she was only about 1 kilometre from her home when she was attacked. He said "every available resource" was being poured into the investigation.