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Results tagged with ramsey-theory
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user 4558
Branch of combinatorics with the philosophy that 'total disorder is impossible'. For example, Ramsey's theorem asserts that for each $n$, every sufficiently large graph either contains a clique of size $n$ or a stable set of size $n$.
2
votes
Proofs of Lower Bounds for Ramsey Numbers?
If I am understanding the jist of your second argument, some might say that it is essentially the same as the first. Pigeonhole principle and probabilistic method both boil down to indirect existance …
- 7,857
27
votes
1
answer
3k
views
Monochromatic triangles in every two-coloring of the plane?
An old problem (possibly due to Erdős and Graham?): given a triangle $T$ and a two-coloring of the plane, does there necessary exist a monochromatic congruent copy of $T$? Here "monochromatic" means …
- 7,857