I've heard that running in a zig-zag pattern makes it more difficult for the alligator to keep up with you. Is that true?
Just run. Alligators (and crocodiles) are cold blooded and as a result don't have a lot of stamina. Warm blooded animals can maintain high energy output for longer periods.
If you want to aim for something other than 'away from the alligator', go for high ground. That will lessen your chance of ending up in the water where the gator has a better chance of catching you.
They can't run for long periods. They have brief sprints up to about 12mph so you can outrun one, especially if you keep going.
That said, alligators don't attack humans. From this LA Times article:
Alligator attacks are still extremely rare. In fact, the likelihood of a Florida resident being injured in an unprovoked alligator attack is roughly one in 2.4 million, according to the Florida Fish and Wildlife Conservation Commission.
But if you do provoke one, all the advice suggests forgetting about swerving - just run fast, and away from water.