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Could you explain, step by step, how to check the in-degree and out-degree conditions for Euler walks in directed graphs, including when in-degree equals out-degree at every vertex and when exactly two vertices differ by one?

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Could you go through this question

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Is it always the case that strong components are maximal and disjoint?

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Is it always the case that strong components are maximal and disjoint?

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Could you explain this question as well, I don't fully understand the part where Hamilton cycle requires the vertices to be adjacent.

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Lastly, just a general question, but how would you recommend us to prepare to be able to answer any sort of proof questions in the exam

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Lastly, just a general question, but how would you recommend us to prepare to be able to answer any sort of proof questions in the exam