The fewest number of colors necessary to color a Graph or surface. The
chromatic number of a surface of Genus is given by the Heawood Conjecture,

where is the Floor Function. is sometimes also denoted . For , 1, ..., the first 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 so that no two Edges incident on the same Vertex have the same color is called the ``Edge chromatic number.''

**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. Sequence
A000934/M3292
in ``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.

© 1996-9

1999-05-26