How did King Laius get by the Sphinx?

Those familiar with the tale of Oedipus know that Oedipus slew his father, King Laius, where three roads meet some distance from the city of Thebes. My question is how did King Laius get past the Sphinx guarding the city gate? Or was it not rather the case that he went on embassy to Delphi before the Sphinx arrived at the city and was returning home at the time of his fatal encounter with Oedipus? I have read sources from Homer to Seneca and modern day anthologies of Greek mythology without discovering the answer.

Not that this may help you right now, but from what I understand, the Spinx came after King Laius. Remember, Oedipus was married to Jocasta when he was made King. They would have not done either of those if they didn't know that Laius was already dead. Now, the hearld told them the story after he came back to town, where upon Oedipus was already named King. So you have to assume that everyone knew the King was dead, just did not know what happened. This gives proof that whether through knowledge passed to them or Oracles, everyone knew the King was dead. Then again...perhaps Sochocles merly forgot this part and this happens to be a plot hole.

It seems logical that only after the leading powerful authority figure with sway over an army leaves (the said King), would a ferocious beast set up camp.