Eurymachus (Ancient Greek: Εὐρύμαχος), son of Polybus, is one of the two leading suitors of Penelope in Homer's Odyssey, beside Antinous. Smooth-tongued and deceitful, he flatters Telemachus in public while plotting his death, lies with the maid Melantho, and after Antinous falls tries in vain to buy Odysseus off with restitution before he is shot down.
Adapted from Wikipedia, "Eurymachus (Odyssey)" · CC BY-SA 4.0
I.Leader among the wooers
Eurymachus acts as a leader through charisma rather than open violence. The men of Ithaca look upon him almost as a god; Eumaeus names him the wooer most eager to marry Penelope and inherit Odysseus' honour. He outdoes the others in gift-giving, and Penelope's kin are said to favour the match.
He shows no regard for xenia, consuming the house without reciprocation. With Antinous he plots Telemachus' murder at sea; to Penelope he swears a lying oath that no man will lay hands on the prince while he yet breathes. Melantho, reared by Penelope, is his lover and mistress.
II.Death
He jeers at the disguised Odysseus, hurls a footstool that strikes a cup-bearer instead, and with Antinous persists longest at Penelope's bow without stringing it. When Odysseus reveals himself and Antinous falls first, Eurymachus alone tries words: he blames the dead chief for all the trouble and offers to repay wine, food, bronze, and gold.
Odysseus refuses. Eurymachus draws his sword and charges; an arrow in the chest stops him among the first slain.