At 12.47pm South Wales Police received a report that a woman in Allensbank Road has been assaulted and suffered a neck wound.
A second report was received at 12.51pm that a man had been assaulted in Tewkesbury Street.
The woman, who is in her 60s, was described as conscious and breathing at the scene and was taken to the University Hospital of Wales, Cardiff, for treatment. There is no update on her current condition.
The male victim, who is in his 30s, was described as being in shock after suffering facial injuries.
A man was arrested in Dalton Street at 1.12pm and a knife has been recovered.
More top news
Ron Jones survived Auschwitz and has supported the Poppy Appeal for over four decades. Today he celebrates his centenary.
A windy day, with rain gradually spreading from the south-west further into the rest of the country.
A man and two teenagers have been arrested after a man was stabbed to death in Rhyl in the early hours of this morning.