Conjecture a necessary condition for a graph to have an, Mathematics

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Conjecture a necessary condition for a graph to have an

1. Conjecture a necessary condition for a graph to have an Euler circuit (i.e., if a graph has an Euler circuit, this condition must hold).

2. Make a conjecture about what property (or properties) a graph needs to have (or not have) for it to be guaranteed to have an Euler circuit.

3. Make similar conjectures about Euler traversals.

4. Try to prove your conjectures.

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