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(c) Marian Olejar, Jr., 2005-2007
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chromatic number of surface
Author: Marian Olejar, Jr. Created: Nov/10/2006 Last edit: Nov/10/2006
graph theory, topology:
The chromatic number of the surface S (usually denoted chr(S)) is the minimum number of colors needed to color any map corresponding to a 2-cell imbedding of a graph into surface S. Other definition can be: The chromatic number of the surface S is the maximum of the set of chromatic numbers of graph that can be imbedded (embedded) in surface S. The solution of Heawood map-coloring prblem (created by Ringel-Young in 1968): for genus `g>=1`: `chr(S_g) = |__ ((7+sqrt(1 + 48g))/(2)) __|` Cite this article as: Marian Olejar, Jr.: chromatic number of surface from VeryPrime's Dictionary of mathematics Link to this page: http://www.veryprime.com/dict/chromatic_number_of_surface.php |