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Results tagged with ramsey-theory
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user 468
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
Accepted
Permutations of Grid Colorings
O(1) is impossible even if you drop the condition of no monochromatic rectangles, and even if you know that the two cells are always chosen within a given row.
Suppose the length of the rows, $m$, …
- 6,327
2
votes
Bound on cardinality of a union
There is the obvious lower bound of nN - {n \choose 2}N_2.
(I'm taking N_2 to be the bound on the size of an intersection of 2 sets; I'm not sure if that's what you meant.)
I don't think it's poss …
- 6,327
5
votes
Bound on cardinality of a union
A better solution than my previous one is
max_{1\leq i \leq n} iN - {i \choose 2}N_2
(That is to say, we can simply consider only i of the sets instead of all n of them, and then apply my previous …
- 6,327