Chromatic Number
The fewest number of colors 
necessary to color a Graph or surface. Thechromatic number of a surface of Genus 
is given by the Heawood Conjecture,
where
is the Floor Function. 
is sometimes also denoted 
. For 
, 1, ..., thefirst few values of are 4, 7, 8, 9, 10, 11, 12, 12, 13, 13, 14, 15, 15, 16, ... (Sloane's A000934).The fewest number of colors necessary to color each Edge of a Graph sothat no two Edges incident on the same Vertex have the same color is called the``Edge chromatic number.''
See also Brelaz's Heuristic Algorithm, Chromatic Polynomial, Edge-Coloring, Euler Characteristic,Heawood Conjecture, Map Coloring, Torus Coloring
References
Chartrand, G. ``A Scheduling Problem: An Introduction to Chromatic Numbers.'' §9.2 in Introductory Graph Theory. New York: Dover, pp. 202-209, 1985. Eppstein, D. ``The Chromatic Number of the Plane.''http://www.ics.uci.edu/~eppstein/junkyard/plane-color/. Sloane, N. J. A. SequenceA000934/M3292in ``An On-Line Version of the Encyclopedia of Integer Sequences.''http://www.research.att.com/~njas/sequences/eisonline.html and Sloane, N. J. A. and Plouffe, S.The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995.
- Morrie's Law
- Morse Inequalities
- Morse Theory
- Morse-Thue Sequence
- Mortal
- Mortality Problem
- Morton-Franks-Williams Inequality
- Mosaic
- Moser
- Moser's Circle Problem
- Moss's Egg
- Motzkin Number
- Moufang Plane
- Mousetrap
- Mouth
- Moving Average
- Moving Ladder Constant
- Moving Sofa Constant
- Mrs. Perkins' Quilt
- Much Greater
- Much Less
- Mu Function
- Muirhead's Theorem
- Muller's Method
- Mulliken Symbols