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Apply four color theorem to the map of Florida?

I'm attempting to apply the Four Color Theorem to a map of Florida and I'm following an example available among the standard collection of examples located at: ref/GeoGraphics; "Neat Examples" (provided by my Mathematica software). Unfortunately; the following: 

EntityProperty["AdministrativeDivision", "BorderingCounties"]

doesn't work when I evaluate it using my Mathematica software. I found an alternative way to get around this difficulty and I can apply the four color theorem to subareas of the map of Florida but, the same code that I use for the subareas will not work for the whole state. I have built the attached Mathematica notebook explaining my problem in detail. Thank you for your help!

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POSTED BY: Gilmar Rodriguez-Pierluissi
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Here's a very compact solution using IGraph/M's IGVertexColoring function.

counties = EntityList@EntityClass["AdministrativeDivision", "USCountiesFlorida"];

borderingQ[c1_, c2_] := MemberQ[c1["BorderingCounties"], c2]

graph = RelationGraph[borderingQ, counties];

GeoGraphics@
 MapThread[{GeoStyling[#2], Polygon[#1]} &, {counties, ColorData[97] /@ IGVertexColoring[graph]}]

Mathematica graphics

?IGVertexColoring

IGVertexColoring[graph] returns a vertex colouring of graph.

Currently this function does not guarantee a minimum colouring, but it does well here. You can see the fifth colour (purple) around the quintipoint in the South East.
POSTED BY: Szabolcs Horvát

Thank you Chris Hurst for your discussion about quintipoints and your incredible code to build the map of the USA. I wish I had read your posts before learning about quintipoints the hard way! And thank you Aeyoss Antelope for your wonderful sense of humor! Google (and other corporate) interviewees; beware about your "IQ" ; i.e., beware about the "Infamous Quintipoint" question! LOL.
POSTED BY: Gilmar Rodriguez-Pierluissi

Thanks for this! I forgot about the quintipoint, making this into a Google Corp interview question...

Interviewer: How would you make a four-color map of the counties of the state of Florida?

Applicant: It is not possible because of the quintipoint! Hahaha
POSTED BY: Aeyoss Antelope
Greg Hurst
Greg Hurst
Posted 9 years ago
POSTED BY: Greg Hurst

@Aeyoss Antelope: Yes Aeyoss; that is indeed the example that I'm emulating; with counties in Florida instead of countries in Europe. Thank you.
POSTED BY: Gilmar Rodriguez-Pierluissi
POSTED BY: Aeyoss Antelope

@Joel Gilly Thank you for responding to my query. I have no trouble getting the list of counties as you described. The trouble occurs when attempting to color the counties as described in another Mathematica notebook located at: http://community.wolfram.com/groups/-/m/t/1097057 Thank you for your help!
POSTED BY: Gilmar Rodriguez-Pierluissi
Joel Gilly
Joel Gilly, None
Posted 9 years ago

I am going to assume that in your solution you want a nested list of string values that represent the Counties with which you are interested. In that case, you will need to apply the EntityValue function to a valid Entity Data Types. However, you will first need to obtain an Entity Class from your strings that represent the Entity Types you seek. 

xx = EntityValue[
   EntityClass["AdministrativeDivision", "USCountiesFlorida"], 
   "BorderingCounties"];

EntityValue[#, "Name"] & /@ xx
POSTED BY: Joel Gilly
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