Difference between revisions of "Hadwiger-Nelson problem"

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(Created page with "The Chromatic Number of the Plane (CNP) is the chromatic number of the graph whose vertices are elements of the plane, and two points are connected by an edge if they are a un...")
 
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== Wikipedia ==
 
== Wikipedia ==
  
* [https://en.wikipedia.org/wiki/Hadwiger%E2%80%93Nelson_problem]
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* [https://en.wikipedia.org/wiki/Hadwiger%E2%80%93Nelson_problem Hadwiger-Nelson problem]
 
* [https://en.wikipedia.org/wiki/Lov%C3%A1sz_number Lovasz number]
 
* [https://en.wikipedia.org/wiki/Lov%C3%A1sz_number Lovasz number]
 
* [https://en.wikipedia.org/wiki/Moser_spindle Moser spindle]
 
* [https://en.wikipedia.org/wiki/Moser_spindle Moser spindle]

Revision as of 12:21, 13 April 2018

The Chromatic Number of the Plane (CNP) is the chromatic number of the graph whose vertices are elements of the plane, and two points are connected by an edge if they are a unit distance apart. The Hadwiger-Nelson problem asks to compute CNP. The bounds [math]4 \leq CNP \leq 7[/math] are classical; recently [deG2018] it was shown that [math]CNP \geq 5[/math].



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Bibliography

  • [deG2018] [The chromatic number of the plane is at least 5, Aubrey D.N.J. de Grey, Apr 8 2018.
  • [P1998] D. Pritikin, All unit-distance graphs of order 6197 are 6-colorable, Journal of Combinatorial Theory, Series B 73.2 (1998): 159-163.