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arXiv · 1509.01595

The vector graph and the chromatic number of the plane, or how NOT to prove that $χ(\mathbb{E}^2)>4$

Jeremy F. Alm·Jacob Manske
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Abstract

The chromatic number $χ\left(\mathcal{E^2}\right)$ 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 $χ\left(\mathcal{E^2}\right)$ by pasting Moser Spindles together, even countably many.

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Jeremy F. Alm, Jacob Manske. 2016-08-04. The vector graph and the chromatic number of the plane, or how NOT to prove that $χ(\mathbb{E}^2)>4$. https://arxiv.org/abs/1509.01595

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