Question: Does the slang term "Bogart" (don't Bogart the pizza for example) have anything to do with Humphrey Bogart? 

Answer: yes, when bogart's movie characters would smoke a cigarette, they would often let it hang on their lips for a long time, not really smoking it, but it would burn up just the same and, in a sense, be wasted.  the term was originally applied to toking (smoking a marijuana cigarette) as in "don't bogart that joint" meaning don't waste it, if you're not going to smoke it, give it to me so i can have some, instead of just letting it burn up.  i haven't heard it applied to pizza, but the same principle applies, don't hog the whole pizza and let it get cold, pass it to me so i can have some while it's still hot
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