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Strengthen your inductive hypothesis
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[QUICK DESCRIPTION] Suppose that you are trying to prove by induction that the statement $P(n)$ holds for every positive integer $n$, and suppose that you are having difficulties deducing $P(n)$ from $P(n-1)$. One option you have is to work on a different statement $Q(n)$. If $Q(n)$ implies $P(n)$ and if $Q(n)$ can be proved by induction, then you have proved $P(n)$. This often turns out to be a very helpful technique. [PREREQUISITES] Basic graph theory. [EXAMPLE thomassen|Proof that all planar graphs are 5-choosable] [GENERAL DISCUSSION]
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