Unit Distance Graphs with Ambiguous Chromatic Number
نویسنده
چکیده
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 Rn, and hence may be seen as further evidence that the chromatic number of the plane might depend on set theory.
منابع مشابه
A Unit Distance Graph with Ambiguous Chromatic Number
Saharon Shelah and Alexander Soifer recently presented some 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 famous Chromatic Number of the Plane problem. In this paper a new example of a graph with ambiguous chromatic number is presented. This graph is a unit distance graph in the plane and hence...
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ورودعنوان ژورنال:
- Electr. J. Comb.
دوره 16 شماره
صفحات -
تاریخ انتشار 2009