Unit distance graphs with ambiguous chromatic number

Michael Stuart Payne

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First LA aszlA o SzA ekely 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 Rn, and hence may be seen as further evidence that the chromatic number of the plane might depend on set theory.
Original languageEnglish
Pages (from-to)1 - 7
Number of pages7
JournalElectronic Journal of Combinatorics
Issue number1
Publication statusPublished - 2009

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