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Results tagged with probabilistic-method
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user 497926
Probabilistic methods prove existence results in a nonconstructive fashion, by showing the chance of randomly selecting a solution is greater than zero.
3
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Probabilistic method Alon and Spencer Azuma's inequality
Theorem 7.5.2 states:
Let $v_1, \dots, v_n$ be vectors with $\|v_i\| \leq 1.$ Let $\epsilon_1, \dots, \epsilon_n \in \{-1, 1\}$ be independent with uniform probability and let $X=\|\epsilon_1 v_1 + \d …
4
votes
1
answer
149
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For every partition of $E(K_{n,n})$ into $n$ colour classes of size $n$, there is a vertex i...
Given a partition of the edges of $K_{n,n}$ into $n$ colours, where each colour appears exactly $n$ times, prove that there exists a vertex incident to at least $\sqrt{n}$ colours.