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Probabilistic methods prove existence results in a nonconstructive fashion, by showing the chance of randomly selecting a solution is greater than zero.

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For every partition of $E(K_{n,n})$ into $n$ colour classes of size $n$, there is a vertex i...

Here is a short proof. Thanks to David Speyer for simplifying an earlier proof of mine (see the comments below). For each colour $i \in [n]$, let $a_i$ be the number of vertices incident to an edge of …
Tony Huynh's user avatar
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