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A Hamiltonian cycle is a graph cycle (i.e., closed loop) through a graph that visits each...

A Hamiltonian cycle is a graph cycle (i.e., closed loop) through a graph that visits each vertex exactly
once. A graph is called Hamiltonian if it contains a Hamiltonian cycle. Suppose a graph is composed of
two components, both of which are Hamiltonian.

Find the minimum number of edges that one needs to add to obtain a Hamiltonian graph. Prove your answer.

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