Abstract
Two regions are adjacent if they share a common boundary that isn’t a corner, where corners are the points shared by three or more regions. Figure 18.1 is a map of a portion of Europe, consisting of Portugal, Spain, France, Holland, Belgium, Luxembourg, Switzerland, and Italy. Which countries share a common border and must be assigned different colors? One way to color the map in such a way that no adjacent countries share the same color is to assign Portugal purple; Spain and Italy pink; France and Holland blue; Belgium yellow, Luxembourg green: and Switzerland brown.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Articles
Appel, K., & Haken, W. (1977). Solution of the four color map problem. Scientific American, 237(4), 108–121.
Appel, K., & Haken, W. (1989). Every planar map is four-colorable. Providence, RI: American Mathematical Society.
Applications of the Four Color Problem www.researchgate.net/publication/255643652_Applications.
Nowlan, Robert A. (n.d.). Augustus De Morgan. In A chronical of mathematical people. www.robertnowlan.com
De Morgan, A. (1833). On teaching arithmetic. Quarterly Journal of Education.
De Morgan’s laws www.en.wikipedia.org/wiki/De_Morgan%27s_laws
Four-color problem www.daviddarling.info/encyclopedia/F/four-color_problem.html
The Four-Color Problem: Concept and Solution www.math.wustl.edu/~sk/4-color.pdf
Maritz, P., & Mouton, A. (2012). Francis Guthrie: A colorful life. Mathematical Intelligencer, 34(3), 67–75.
Monthly Notices of the Royal Astronomical Society, Augustus de Morgan’s obituary written by A. C. Ranyard, February 9, 1872, Vol. XXII p. 112 .
Ranyard, A. C. (1872, February 9). Augustus de Morgan’s obituary. Monthly Notices of the Royal Astronomical Society, XXII, 112.
The Notorious Four-Color Problem www.math.ku.edu/~jmartin/MiniCollege2013/handout.pdf
Books
Barnette, D. (1983). Map coloring, polyhedra, and the four-color problem. Washington, DC: Mathematical Association of America.
De Morgan, A. (1872). A budget of paradoxes. London: Longmans, Green.
De Morgan, A. (1902). On the study and difficulties of mathematics. Chicago, IL: Dover.
De Morgan, A. (1914). Essays on the life and work of Newton. Chicago, IL: Open Court Publishing Company.
De Morgan, A. (2003). Formal logic: The calculus of inference, necessary and probable. Honolulu, HI: University Press of the Pacific.
Katz, V. J. (2000). Using history to teach mathematics: An international perspective. Cambridge: Cambridge University Press.
Ore, Ø. (2011). The four-color problem. New York, NY: Academic Press.
Wilson, R. J. (2002). Four colors suffice: How the map problem was solved. Princeton, NJ: Princeton University Press.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2017 Sense Publishers
About this chapter
Cite this chapter
Nowlan, R.A. (2017). Map Coloring. In: Masters of Mathematics. SensePublishers, Rotterdam. https://doi.org/10.1007/978-94-6300-893-8_18
Download citation
DOI: https://doi.org/10.1007/978-94-6300-893-8_18
Publisher Name: SensePublishers, Rotterdam
Online ISBN: 978-94-6300-893-8
eBook Packages: EducationEducation (R0)