Crossword Genius

Great boxer associated with graduates – or one associated with thieves (3,4)

Ross

I believe the answer is:

ali baba

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'graduates aeur or one associated with thieves' is the definition.
I can't judge whether this defines the answer.

'great boxer associated with' is the wordplay.
'great' becomes 'baba' (I am not sure about this - if you are sure you should believe this answer much more).
'boxer' becomes 'Ali' (Muhammad Ali).
'associated with' is a charade indicator (letters next to each other).
'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 "Pantomime hero opposed by forty thieves" , "Hero of Arabic story" , "Pantomime hero who defeated forty thieves" , "Pantomime character who took on 40 thieves" , "fictional character)" .)

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