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The question is: "Prove that if G is a connected planar simple graph, then G has a vertex of degree at most five."

It baffles me because a connected planar simple graph CAN have a vertex of degree more than five.

Am I misunderstanding the wording?

I mean what if I just draw a hexagon with 6 vertices and connect them all to a 7th vertex in the centre?

potatoguy
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    Note that the question asks for "a vertex" to have degree less than six, rather that for every vertex to have small degree. – Mark Bennet Dec 01 '17 at 07:38
  • In your example, the first six vertices each have degree 3. There need only be one vertex with degree less than 6. – JOF14 Dec 01 '17 at 07:39

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