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Hints for Networks

The number of odd vertices (intersections) in a network must be even if it is to be traveled in one journey.

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A network with all even vertices can always be traveled in one journey.

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If a network contains 2, and only 2, odd vertices it can be traveled in one journey, but it is impossible to end up at the starting point. You must start your journey at an odd vertex and end at the other odd vertex.

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If a network contains 4, 6, 8, 10, or any larger even number of odd vertices it is impossible to travel it in one journey. The number of journeys required is equal to half the number of odd vertices.

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