Re: Map Colors (was: Re: New <AREA> syntax proposal)

Jeff de la Beaujardiere (delabeau@iniki.gsfc.nasa.gov)
Wed, 11 Jun 1997 09:26:58 -0400


Date: Wed, 11 Jun 1997 09:26:58 -0400
Message-Id: <199706111326.JAA00049@iniki.gsfc.nasa.gov>
From: Jeff de la Beaujardiere <delabeau@iniki.gsfc.nasa.gov>
To: w3-html-list@faerber.muc.de, www-html@w3.org
Subject: Re: Map Colors (was: Re: New <AREA> syntax proposal)


I think I'm partially to blame for starting this thread debating the number
of colors needed in a map.  Colin F Reynolds wrote, "Don't most area maps
use four colo(u)rs, that being the maximum number of colors required to
assure that no two adjacent regions bear the same color?"  I replied that
"Four is the *minimum*, which is probably what you meant to write."

I think we all agree that 4 is the magic number here, but some say it's the
minimum and others the maximum.  The debate is linguistic rather than
mathematical: there is ambiguity in the English language which leads to some
confusion.  The phrase "maximum number of colors required" does not make it
clear whether the adjective "required" refers to "number" or "colors."

To color an arbitrary map, you need at least 4 colors.
In that sense, 4 is the 
"minimum required number of colors".  But 4 is also the 
"maximum number of required colors", all other colors being optional.

Put another way, if you list the requirements for all possible maps, the
requirement is never greater than 4, so 4 is the maximum.  But except for
the simplest maps, 4 colors are essential, so 4 is the minimum.  I think
stating that 4 is the minimum best conveys the idea that you need at least 4
colors.

Hoping to kill the thread by posting "one last time, I swear!",
Jeff

  = J-F Pitot de La Beaujardiere
  = delabeau@iniki.gsfc.nasa.gov
  = http://globe2.gsfc.nasa.gov/