Talk:Route inspection problem

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Is the information here relevance to the "route inspection problem"? It seems a little bit off topic to me. Dysprosia 11:23, 2 Oct 2003 (UTC)

The article says:

It should, however, be noted, that this is only a condition that ensure that a Hamiltonian cycle exist, we cannot conclude the other way

but above it, it says "if and only if". Which is it?

It is not about Hamiltonian (going through nodes) but about Eulerian (going through edges) cycles. A non-oriented connected graph G=(V,E) has an Eulerian cycle if and only if all nodes have even degree.