Cychreus was a demigod and a son of Poseidon.
Cychreus was the son of Poseidon and Salamis, daughter of the River god Asopus.
Depending upon the version of the myth, Cychreus either became the king of Salamis, or else went on a rampage there, because of his hotheaded nature, and was driven away by Eurelochus.
Either way, a dragon clearly named after Cychreus is involved. Either Cychreus is known as "the dragon" for his short temper, or there is a dragon named Cychreides who rampages in Cychreus' place. If there is a separate dragon, then Cychreus slays it and gets voted king, or else Eurelochus drives it away.
In some versions, Cychreus has sex with the nymph Stilbe, and became the father of Chariclo, Chiron's wife. One of his daughters, Glauce married Telamon. Telamon eventually inherited Cychreus' kingdom after his wife died.