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Diffstat (limited to 'ps5/main.tex')
| -rw-r--r-- | ps5/main.tex | 2 |
1 files changed, 1 insertions, 1 deletions
diff --git a/ps5/main.tex b/ps5/main.tex index 662ffa1..b04f24e 100644 --- a/ps5/main.tex +++ b/ps5/main.tex @@ -313,7 +313,7 @@ concludes the proof of the question. \paragraph{(e)} Using Markov's inequality, let $X$ be the number of monochromatic edges after applying the previous rounding scheme. We have: \begin{displaymath} - \Pr\left[X\geq \frac{n}{4}\left] \leq \frac{n/6}{n/4} = \frac{2}{3} + \Pr\left[X\geq \frac{n}{4}\right] \leq \frac{n/6}{n/4} = \frac{2}{3} \end{displaymath} Hence, by repeating the previous rounding scheme $O(\log n)$ times, we know that at least once we will have less that $\frac{n}{4}$ monochromatic edges |