Geodesic
Unit distance graphs with ambiguous chromatic number
The electronic journal of combinatorics, Tome 16 (2009) no. 1
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First László Székely 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 ${\Bbb R}^n$, and hence may be seen as further evidence that the chromatic number of the plane might depend on set theory.
DOI : 10.37236/269
Classification : 05C15, 05C12
Mots-clés : Chromatic Number of the Plane problem, infinite graphs, ambiguous chromatic number, unit distance graphs 
@article{10_37236_269,
     author = {Michael S. Payne},
     title = {Unit distance graphs with ambiguous chromatic number},
     journal = {The electronic journal of combinatorics},
     year = {2009},
     volume = {16},
     number = {1},
     doi = {10.37236/269},
     zbl = {1185.05063},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/269/}
}
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Michael S. Payne. Unit distance graphs with ambiguous chromatic number. The electronic journal of combinatorics, Tome 16 (2009) no. 1. doi: 10.37236/269

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