It is possible for a graph with all vertices of even valence to NOT have an Euler circuit.

Name: It is possible for a graph with all vertices of even valence to NOT have an Euler circuit.
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Question

Quizplus · Accepted Answer

The graph could have multiple connected components or be disconnected, which would prevent an Euler circuit from existing. For example, consider a graph with two disconnected components, each consisting of a single vertex with valence 2. This graph has all even valence vertices but no Euler circuit.

It Is Possible for a Graph with All Vertices of Even