Graduates tracking the greatest caveman? (3,4)

I believe the answer is:
ali baba
'caveman?' is the definition.
The definition and answer can be both people as well as being singular nouns.
Maybe you can see an association between them that I don't see?
'graduates tracking the greatest' is the wordplay.
'graduates' becomes 'baba' (I can't justify this - if you can you should give a lot more credence to this answer).
'tracking' means one lot of letters go next to another (track can mean to follow or go after).
'the greatest' becomes 'Ali' (Muhammad Ali was known as the Greatest).
'baba' put after 'ali' is 'ALI BABA'.
Can you help me to learn more?
(Other definitions for ali baba that I've seen before include "PANTO (part title)" , "Arabian Nights character" , "He got involved with forty thieves" , "Pantomime character who took on 40 thieves" , "With 40 thieves, he's a fictional woodcutter" .)
