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What are the theorems/results/widely applicable results in graph theory that everyone should know about?

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    I think this should be made community wiki, perhaps with one result per answer.2011-03-11
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    I would like to but there is no option available.2011-03-11
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    I am slightly skeptical about this question, although I left an answer. Do you want this to just turn into a list of everyone's favorite results in graph theory (which is trivial to generate: just go through any good book), or do you want to actually give some criteria for what counts as "important"?2011-03-11
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    I want a list of most frequently used results. In the books on graph theory there are thousands of theorems and I am not sure which ones of those I should give importance to.2011-03-11
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    Used where? By whom?2011-03-11
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    mathematicians, computer scientists, anyone...?2011-03-11
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    "Mathematicians" is an enormous group of people, some of whom are graph theorists and may use _all_ of the results in your books.2011-03-11

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