Inquiries are continuing into the death of Ashling Murphy, with Gardaí shifting their attention to a bicycle believed to be linked to the incident.
A man who was arrested yesterday and questioned about the fatal attack on the 23-year-old has been eliminated as a suspect.
Gardaí are appealing to the public to share any information on a black "Falcon Storm" mountain bike with distinctive yellow/green front forks and straight handlebars.
Frank Kelly is the retired principal of Durrow National School, where Ashling taught.
He says the local children remember their teacher as "a joy" and slow to anger.
"If you got something wrong she wouldn't give out to you she'd just show you how to do it again. And I suppose that sums up the lovely girl we had."
In the wake of the attack, calls are growing for a complete review of sentencing in cases of male violence against women.
Anne Clarke, Manager of Offaly Domestic Violence Support Services, says many people serve just a third of their sentences.
She says by letting people off early, the system enables perpetrators.