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

Jeremy F. Alm; Jacob Manske

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

Combinatorics 2016-08-08 v2

Authors: Jeremy F. Alm , Jacob Manske

Abstract

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

Keywords

chromatic number of the plane Moser spindle vector graph lower bound graph coloring Euclidean plane

Cite

@article{arxiv.1509.01595,
  title  = {The vector graph and the chromatic number of the plane, or how NOT to prove that $\chi(\mathbb{E}^2)>4$},
  author = {Jeremy F. Alm and Jacob Manske},
  journal= {arXiv preprint arXiv:1509.01595},
  year   = {2016}
}

Comments

To appear in Australasian Journal of Combinatorics

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

Abstract

Keywords

Cite

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