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.
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The tree was blown down in a gale in February after standing for more than 200 years.
Aberdaron recorded wind speeds of 70mph this morning. A warning is issued covering the whole of Wales.