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a/Writerside/topics/04/Theoretische Informatik/01Einleitung.md b/Writerside/topics/04/Theoretische Informatik/01Einleitung.md new file mode 100644 index 0000000..ad24932 --- /dev/null +++ b/Writerside/topics/04/Theoretische Informatik/01Einleitung.md @@ -0,0 +1,28 @@ +# Einleitung + +## Das Ampelproblem +![image_553.png](image_553.png) + + +### Lösungsansatz +- ungerichteter Graph $G = (V, E)$ + - V = endliche Knotenmenge + - E = endliche Kangenmenge + +> Graph G=(V,E) für kommende Abbildung: +> V = {s1, s2, s3, s4, s5, s6}, +> E = {{s1, s4}, {s1, s5}, {s2, s4}, {s2, s5}, {s3, s6}, {s4, s5}} + +![image_554.png](image_554.png) + +#### Clique C +nicht-leere Teilmenge $C \subseteq V$, wenn zwei verschiedene Knoten in C paarweise durch eine Kante aus E verbunden sind + +**Es gilt:** +${u,v} \in E$ für alle $u,v \in C$ mit $u \ne v$ + +per Definition ist **auch jede einelementige Teilmenge** $C \subseteq V$ eine Clique + +Größe einer Clique: +$|C|$ +