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Here I asked how I can write a particular 4-cycle as a product of simple 4-cycles and I understand the solutions given. I now want to prove that every 4-cycle can be written as the product of simple 4-cycles. The only way that I know of to prove this is induction. I have no problem with induction but my problem is that I can not come up with a good statement for induction that I can prove. So can you please give me some hints on this?

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    It isn't true in $S_4$.2011-03-23
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    What about $S_n$ when $n\geq5$?2011-03-23
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    What is a "simple" $4$-cycle? What other kinds of $4$-cycles are there?2018-10-15

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