Difference between revisions of "Hadwiger-Nelson problem"

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== Bibliography ==
 
== Bibliography ==
  
* [deG2018] [[https://arxiv.org/abs/1804.02385 The chromatic number of the plane is at least 5], Aubrey D.N.J. de Grey, Apr 8 2018.
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* [deG2018] A. de Grey, [[https://arxiv.org/abs/1804.02385 The chromatic number of the plane is at least 5]], arXiv:1804.02385
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* [H1945] H. Hadwiger, Uberdeckung des euklidischen Raum durch kongruente Mengen, PortugaliaeMath. 4 (1945), 238–242.
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* [MM1961] L. Moser and M. Moser, Solution to Problem 10, Can. Math. Bull. 4 (1961), 187–189.
 
* [P1998] D. Pritikin, All unit-distance graphs of order 6197 are 6-colorable, Journal of Combinatorial Theory, Series B 73.2 (1998): 159-163.
 
* [P1998] D. Pritikin, All unit-distance graphs of order 6197 are 6-colorable, Journal of Combinatorial Theory, Series B 73.2 (1998): 159-163.
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* [S2008] A. Soifer, The Mathematical Coloring Book, Springer, 2008, ISBN-13: 978-0387746401.

Revision as of 12:22, 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] A. de Grey, [The chromatic number of the plane is at least 5], arXiv:1804.02385
  • [H1945] H. Hadwiger, Uberdeckung des euklidischen Raum durch kongruente Mengen, PortugaliaeMath. 4 (1945), 238–242.
  • [MM1961] L. Moser and M. Moser, Solution to Problem 10, Can. Math. Bull. 4 (1961), 187–189.
  • [P1998] D. Pritikin, All unit-distance graphs of order 6197 are 6-colorable, Journal of Combinatorial Theory, Series B 73.2 (1998): 159-163.
  • [S2008] A. Soifer, The Mathematical Coloring Book, Springer, 2008, ISBN-13: 978-0387746401.