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I have to find an example to path of graph that dont have euler path/cycle even tought all his vertices degree is even.

I have an algorithm that return path of graph, starting in random point and follows the next edge without returning to edge that have been passed before. The algoritm stops when vertice have no following edge. I know for sure that this algorith return a cycle since all edges are even but I cant find graph that contradicts the algorithm.

please help me. thank you for your attention!

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Any connected graph in which each vertex has even degree has a Euler cycle.

Try a disconnected graph.

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