Did Cleopatra date with Roman general Julius Caesar when he was in Egypt?

Not sure what the ancient Roman equivalent of 'date' was, but he was romantically involved with her. They had a son, Caesarion, but because Caesar and Cleopatra were not married (and especially because she wasn't Roman), their son was illegitimate; this is why Octavian (who became Augustus) had the most significant claim as Caesar's heir, even though he was an adopted son.