Unit distance graphs with ambiguous chromatic number

Details Unit distance graphs with ambiguous chromatic number Unit distance graphs with ambiguous chromatic number

2007-07-09

arxiv.org/abs/0707.1177v3

Electron. J. Combin. 16 (2009), no. 1, Note 31

Mathematics

Combinatorics

7 pages

Scientific paper

First Laszlo Szekely and more recently Saharon Shelah and Alexander Soifer have presented examples of infinite graphs whose chromatic numbers depend on the axioms chosen for set theory. The existence of such graphs may be relevant to the Chromatic Number of the Plane problem. In this paper we construct a new class of graphs with ambiguous chromatic number. They are unit distance graphs with vertex set R^n, and hence may be seen as further evidence that the chromatic number of the plane might depend on set theory.

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