In Greek mythology we encounter the name Eurytion in two forms - either as a centaur or a giant.
Eurytion as Centaur
Eurytion lived in the mountains of Thessaly and was considered the strongest centaur. One day he and his companions were invited to a wedding by the king of the Lapiths. The centaurs got drunk during the feast and decided to kidnap the newlywed Hippodameia and other women. A fight ensued, in which most of the centaurs fell.
Eurytion as a giant
The giant Eurytion guarded Geryon's herds on the island of Erytheia together with the two-headed dog Orthos. When the hero Heracles tried to steal their herds, they engaged him in battle. They were both killed and then the hero took the herd.