Ramsey's Theorem
A generalization of Dilworth's Lemma. For each 
with 
, there exists a leastInteger 
(the Ramsey Number) such that no matter how the Complete Graph 
istwo-colored, it will contain a green Subgraph 
or a red Subgraph 
. Furthermore,
if
. The theorem can be equivalently stated that, for all 
, there exists an 
such thatany complete Digraph on 
Vertices contains a complete transitive Subgraph of 
Vertices. Ramsey's theorem is a generalization of the Pigeonhole Principle since
See also Dilworth's Lemma, Natural Independence Phenomenon, Pigeonhole Principle, Ramsey Number
References
Graham, R. L.; Rothschild, B. L.; and Spencer, J. H. Ramsey Theory, 2nd ed. New York: Wiley, 1990. Spencer, J. ``Large Numbers and Unprovable Theorems.'' Amer. Math. Monthly 90, 669-675, 1983.
- Medial Pentagonal Hexecontahedron
- Medial Rhombic Triacontahedron
- Medial Triambic Icosahedron
- Medial Triangle
- Medial Triangle Locus Theorem
- Median Point
- Median (Statistics)
- Mediant
- Median (Triangle)
- Mega
- Megistron
- Mehler-Dirichlet Integral
- Mehler Quadrature
- Mehler's Bessel Function Formula
- Mehler's Hermite Polynomial Formula
- Meijer's G-Function
- Meissel's Formula
- Mellin Transform
- Melnikov-Arnold Integral
- Melodic Series
- MEM
- Memoryless
- Menasco's Theorem
- Menelaus' Theorem
- Menger's n-Arc Theorem