State Menger's theorem in both the vertex form and the edge form. Explain briefly how the edge form of Menger's theorem may be deduced from the vertex form.

(a) Show that if $G$ is 3 -connected then $G$ contains a cycle of even length.

(b) Let $G$ be a connected graph with all degrees even. Prove that $\lambda(G)$ is even. [Hint: if $S$ is a minimal set of edges whose removal disconnects $G$, let $H$ be a component of $G-S$ and consider the degrees of the vertices of $H$ in the graph $G-S$.] Give an example to show that $\kappa(G)$ can be odd.