As far as I know, a planar graph is simply defined as a graph that can be drawn in the plane with none of its edges crossing. This I understand.
However, I came across a problem that says: "Every planar graph has a vertex of degree at most five."
In the image above there are nine vertices, one of which has degree 8. None of the edges cross, so why is this not a planar graph?
Best Answer
That theorem is meant to be read as follows: "For all planar graphs G, there exists a vertex $v$ of $G$ with degree $5$ or less." You are reading it as "For all planar graphs G and for all vertices $v$ of $G$, $v$ has degree $5$ or less"