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I need to prove that in every graph $G$ with minimal degree $\delta \geq 2$ there's a cycle of length at least $\delta+1$. I think that it's enough to show the result for $\delta$-regular graphs, but I have no idea how to start. Any hints (not full solutions) or ways to approach it will be appreciated.

sel
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'Would you tell me, please, which way I ought to go from here?'

'That depends a good deal on where you want to get to,' said the Cat.

'I don't much care where — ' said Alice.

'Then it doesn't matter which way you go,' said the Cat.

'— so long as I get somewhere,' Alice added as an explanation.

'Oh, you're sure to do that,' said the Cat, 'if you only walk long enough.'

Alex Ravsky
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