The vector graph and the chromatic number of the plane, or how NOT to prove that χ(E²)>4

الأصل · EN

The chromatic number χ(E²) of the plane is known to be some integer between 4 and 7, inclusive. We prove a limiting result that says, roughly, that one cannot increase the lower bound on χ(E²) by pasting Moser Spindles together, even countably many.