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  1. Is there any graph $G$ with $\kappa(G) < \lambda(G) < \delta(G)$?

  2. Is there a graph which has a Euler circuit but no Hamilton Cycle?

$\kappa(G)$ is the vertex connectivity, $\lambda(G)$ is the edge connectivity and $\delta(G)$ is the minimum degree.

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I don't know the standard notation in this case, please edit it if these changes aren't right. – Ian Mateus Nov 16 '13 at 18:09
up vote 1 down vote accepted

Here is the answer but I recommend you to think once more and then look at the answers. IMO it is very important to try to imagine the graphs for yourself.

For the first part:

enter image description here

For the second part of your question:

Eulerian but not Hamiltonian

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It might be good to have a look at – hhsaffar Nov 16 '13 at 20:13

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