Talk:Hadwiger–Nelson problem

message: Colleagues, in the 1991 paper, and now "The Mathematical Coloring Book: Mathematics of Coloring and the Colorful Life of Its Creators" (Springer, NY, 2009), Alexander Soifer proved that this problem was created in Oct-Nov 1950 by Edward Nelson alone. Even Hadwiger admits that in his 1961 paper. Paul Erdos in his 1994 talk at FAU agreed with Soifer's attribution. It is certainly important to change everywhere, the title included, to The Edward Nelson problem.
Also, in the opinion of many, this is one of the premier problems of mathematics, not medium level as indicated here. I suggest to correct.  —Preceding unsigned comment added by Letranger1 (talk • contribs) 02:29, 8 May 2009 (UTC)
replies: text: I changed this to a more specific and better referenced claim. —David Eppstein 22:11, 26 November 2006 (UTC)

text: See first paragraph of the "variations" section. I just added a reference for the claim there, but didn't otherwise change the text that already answers what is known for your question. —David Eppstein 08:01, 17 January 2007 (UTC)
thread_title: Inception

message: I don't see how the hexagonal tesselation works.  If I repeat the given pattern across the plane in the obvious way I
see many same-colored points at distance 1.  There would be dark blue hexagon right at the top, one edge length
away from the leftmost existing dark blue hexagon.  Most likely I'm just missing something, I usually am when I
comment on a math page.  But at any rate it's not clear to me how it works.  --Psellus (talk) 19:52, 12 May 2011 (UTC)
replies: text: The edge length is not 1, it is slightly less than 1/2, so that the diameter of the hexagons (the distance between the farthest two points within a single hexagon) is slightly less than one. With this choice of edge length the closest pair of points in different hexagons with the same color is greater than 1. Maybe it is not sufficiently clear what to do to repeat the pattern? If a hexagon H is on the boundary of the drawing, the color of the neighboring hexagons can be determined by finding another hexagon with the same color as H and using the same pattern. For instance, the color of the hexagon directly above the red hexagon on the top left corner of the diagram is pink, the same as the color of the hexagons directly above the other three red hexagons. So the hexagons of a single color are spaced apart from each other on a big equilateral-triangle grid; you can see two equilateral triangles with red hexagons at their corners and the pattern continues the same way. —David Eppstein (talk) 20:10, 12 May 2011 (UTC)
thread_title: Hexagonal tesselation

message: I added a link to a tool I built for constructing graphs with edges of unit length.  If this is inappropriate feel free to remove.
:I don't think the link is particularly helpful for this problem. (1) any example that requires more than four colors is likely to be huge; (2) your applet doesn't have features for determining the chromatic number of a graph (instead it appears coloring must be done manually, and the default is uncolored); (3) most importantly, your applet doesn't prevent vertices from being placed on top of each other, making it very difficult to build any nontrivial graphs. It also seems problematic with respect to WP:ELNO #11. —David Eppstein (talk) 06:57, 8 August 2012 (UTC)
thread_title:  External Link 

message: In n dimension, the most color is 2n, right?  — Preceding unsigned comment added by 101.10.10.197 (talk) 16:43, 26 July 2014 (UTC)
replies: text: Read the article. Even in three dimensions the exact value is not known: "As with the version on the plane, the answer is not known, but has been shown to be at least 6 and at most 15." —David Eppstein (talk) 18:22, 26 July 2014 (UTC)
thread_title:  n dimension 

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thread_title:  External links modified 

message: In the section "Variations of the problem" the following sentence confused me: "For instance, if a coloring of the plane consists of regions bounded by Jordan curves, then at least six colors are required.". An article by Woodall and an article by Coulson are cited. Now truthfully, the article by Woodall I do not quite understand but both articles do not seem to have the restriction to be "regions bounded by Jordan curves". Woodall gives the restriction "if the sets are either closed or simultaneously divisible into region (in a sense to be made precise)" while Coulson has the restriction "6 colours are necessary for an excluded distance when convex polygonal tiles (all with areagreater than some positive constant) are used as the colouring base". I am not yet convinced that these conditions are the same as regions bounded by Jordan curves. Could someone help convince me or is there a mistake in the article? Thanks!
EMHwiki (talk) 22:11, 27 February 2019 (UTC)
thread_title:  Regions bounded by Jordan curves