Question: Consider n points on the plane such that every point is connected via edges with at least five other points. Show that there must always

Consider n points on the plane such that every point is connected via edges with at least five other points. Show that there must always exist at least five closed paths (i.e. cycles) such that all of them have an even number of edges or all of them have an odd number of edges.

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To solve this problem we need to demonstrate that there always exists at least five cycles all of which consist either of even or odd numbers of edges ... View full answer

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