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I'm trying to prove that a graph with the below properties has an eulerian path.
1. Graph has no self loops or parallel edges.
2. Every two different vertices u and v have an odd number of common neighbor vertices.
I'm thinking about this problem for a whole day and can't manage to prove this. I think that I can prove it if I could prove that every graph with these properties must have odd number of vertices but I can't prove it as well.
1. Graph has no self loops or parallel edges.
2. Every two different vertices u and v have an odd number of common neighbor vertices.
I'm thinking about this problem for a whole day and can't manage to prove this. I think that I can prove it if I could prove that every graph with these properties must have odd number of vertices but I can't prove it as well.
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