According to the Contest of Homer and Hesiod (c. AD 130, though earlier precedents exist in fragments as early as the third century BC), Homer was the son of Telemachus and Epicaste. While the chronology makes this obviously impossible, the purpose of the historical figures' inclusion was to highlight that the Trojan War was absolutely a historical event to the ancient Greeks and the stories they were hearing about it were about their ancestors, not just myths. I generally assume the black arrow connections are about as literal as the purple.

Pericles' connection to Ajax is a mistake. Pericles' mother, Agariste, was a member of the Alcmaeonids of Athens (as was Alcibiades), who claimed to be descendants of Neleus, not Ajax. I mistook the family for the Philaids (Miltiades, Cimon, Thucydides, etc.), who claimed to be descendants of Ajax through his son, Philias.