Question: The USS Patroclus was named after Achillies beloved slain in what war by Hector?

Context paragraphs:
USS Flagg: The USS "Flagg" is a fictional U.S. Navy "Nimitz"-class aircraft carrier from the toy line, comic, and cartoon series.  It is the G.I. Joe Team's primary sea going vessel, and is named for the team's original commanding officer General Flagg (who was slain in combat against Cobra).

Amphimachus (son of Cteatus): In Greek mythology, Amphimachus ( ; Ancient Greek: Ἀμφίμαχος derived from ἀμφί "amphi" "on both sides, in all directions, surrounding" and μαχη "mache" "battle") was the son of Cteatus (son of Actor) and Theronice, daughter of Dexamenus.  He was one of the leaders of the Elean contingent at the Trojan War (the other was Thalpius, son of Eurytus) and was slain by Hector.

USS Argus (PY-14): USS "Argus" (PY-14) was a patrol yacht that saw service in the United States Navy during World War II.  Named for the Argus (a monster with a hundred eyes supposedly slain by the Greek mythological messenger of the gods, Hermes), she was the second U.S. Navy vessel to bear the name.

The Funeral Games of Patroclus: The Funeral Games of Patroclus is a 1778 fresco by Jacques-Louis David.  It shows the funeral games for Patroclus during Trojan War, with his body and Achilles at the foot of the pyre and Hector resting on his chariot on the right.  It was first exhibited at the Palazzo Mancini in Rome in September 1778, where it was a critical success.  It was then lost until 1972, when it was acquired by the National Gallery of Ireland, its present home.

Arcesilaus (mythology): Arcesilaus in Greek mythology was a son of Lycus (or Areilycus) and Theobule, brother of Prothoenor, and was the leader of the Boeotians in the Trojan war.  He led his people to Troy in ten ships, and was slain by Hector.

Euphorbus: Euphorbus (Greek: Εὔφορβος ), the son of Panthous and Phrontis, was a Trojan hero during the Trojan War.  He wounded Patroclus before Patroclus was killed by Hector.  In the fight for Patroclus' body, Euphorbus was killed by Menelaus.  He was apparently one of Troy's finest warriors.  Menelaus later took Euphorbus' shield to the temple of Hera in Argos.  There are some accounts that claim that it was Euphorbus, not Aeneas, Cycnus or Hector, that killed Protesilaus.

Kebriones: In Greek mythology, Cebriones or Kebriones (Κεβριόνης) was the illegitimate son of King Priam of Troy and a slave.  In the "Iliad" he was the half-brother of Hector and his final charioteer during the Trojan War.  Along with Hector and Paris he was part of the division that finally breached the Argive wall.  Patroclus, the Achaean warrior, killed him by throwing a "shining stone," hitting him in the forehead and knocking his eyes out of his head.  The force of the blow flung him from Hector's chariot, leading Patroclus to remark that with his great "diving" ability, he could have satisfied many by diving for oysters in the "storming sea".

USS Patroclus (ARL-19): USS "Patroclus" (ARL-19) was laid down as a United States Navy "LST-542"-class tank landing ship but converted to one of 39 "Achelous"-class repair ship s that were used for repairing landing craft during World War II.  Named for Patroclus (a Homeric character; a beloved of Achilles, slain by Hector while fighting in Achilles’ armor), she was the only US Naval vessel to bear the name.

Achilles: In Greek mythology, Achilles ( , ; ] ) was a Greek hero of the Trojan War and the central character and greatest warrior of Homer's "Iliad".  His mother was the immortal nereid Thetis, and his father, the mortal Peleus, was the king of the Myrmidons.

Memnon (mythology): In Greek mythology, Memnon (Greek: Mέμνων) was an Ethiopian king and son of Tithonus and Eos.  As a warrior he was considered to be almost Achilles' equal in skill.  During the Trojan War, he brought an army to Troy's defense and had killed Antilochus during a fierce battle.  The death of Memnon echoes that of Hector, another defender of Troy whom Achilles also killed out of revenge for a fallen comrade, Patroclus.  After Memnon's death, Zeus was moved by Eos' tears and granted him immortality.  Memnon's death is related at length in the lost epic "Aethiopis", composed after "The Iliad" circa the 7th century BC.  Quintus of Smyrna records Memnon's death in "Posthomerica".  His death is also described in Philostratus' "Imagines".

Supporting paragraphs: USS Patroclus (ARL-19) Achilles
Answer: Trojan War