There are $112$ non-isomorphic $6$-vertex planar connected graphs, $81$ of which are $3$-colorable.
I'm searching for one example of an ($n\geq 6$-vertex planar connected graph:
a) that does not contain an even-vertex wheel graph: (W4, W6, W8, W10, etc.)
b) whose vertices are not $3$-colorable
I know that there are plenty of examples, but I can't come up with any.