Is it true:
there is a simple planar graph $G$ with
minimum degree $4$,
each $2$ vertices of degree $4$ are nonadjacent
$G$ has no vertices of degree $5$.
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user62228
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Does your graph need to be simple? If not, then it is pretty easy to construct such a graph. – user62228 Feb 26 '13 at 08:50
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$G$ is a simple graph. – Engelssina Tasseva Feb 26 '13 at 08:51
