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authorGloria Mundi <gloria@gloria-mundi.eu>2024-11-17 09:43:08 +0100
committerGloria Mundi <gloria@gloria-mundi.eu>2024-11-17 09:43:08 +0100
commit05b8f5e35cc5604f872ea937364f107375a1fd89 (patch)
tree4a4841806b63115a2355f49a7a0e9b32698d99b3 /content/other/other.tex
parent7437e9268925c6550704ea2dde9d6a5f7137f4cc (diff)
give Turán his acute accent
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Falls $x \leq y$, füge Kante $u_x \to v_y$ hinzu.
Wenn Matching zu langsam ist, versuche Struktur des Posets auszunutzen und evtl. anders eine maximale Antikette zu finden.
- \item \textbf{\textsc{Turan}'s Theorem:}
+ \item \textbf{\textsc{Tur\'an}'s Theorem:}
Die Anzahl an Kanten in einem Graphen mit $n$ Knoten der keine clique der größe $x+1$ enthält ist:
\begin{align*}
ext(n, K_{x+1}) &= \binom{n}{2} - \left[\left(x - (n \bmod x)\right) \cdot \binom{\floor{\frac{n}{x}}}{2} + \left(n\bmod x\right) \cdot \binom{\ceil{\frac{n}{x}}}{2}\right]