0
Wegen dem genau wenn müssen wir hier eine Biimplikation zeigen, die Implikation -> verstehe ich, die Summe von jedem Knoten Grad aus einem Graph ist ja 2|E|. Aber die andere Seite muss doch nicht gelten, wenn man jetzt ein Graph mit den zwei Teilgraphen eines Baumes mit 3 Knoten und $K_2$, dann wird die Rechte Bedingung erfüllt, aber es handelt sich nicht um einen Baum. Zu der Aufgabe gibt es auch lösungen (2. Bild), aber ich verstehe die Induktion nicht. Könnte mir bitte jemand erklären wie ich die andere Seite zeige und was mein Denkfehler ist.
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)
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gefragt
henry dutter
Schüler, Punkte: 142
Schüler, Punkte: 142
Schau erstmal, dass Du die Aussage verstehst. Wenn Du einen Beispielgraph diskutieren willst, lade ein Bild hoch und alle Angaben, die in dem Satz vorkommen, dazu. Beachte auch, dass da nicht steht, dass jeder Graph, der die rechte Seite erfüllt, ein Baum ist. Zur Induktion: Fang und sag konkret, wie weit Du kommst, und was konkret Deine erste Frage ist. Ind. Anf. erledigt?
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mikn
05.10.2023 um 12:12
1. Das heißt Äquivalenz und nicht Biimplikation.
2. Da steht nur, dass es einen Baum gibt, nicht dass jeder Graph, der das erfüllt, ein Baum ist. Das ist ein großer Unterschied. Bitte immer genau lesen. ─ cauchy 05.10.2023 um 12:16
2. Da steht nur, dass es einen Baum gibt, nicht dass jeder Graph, der das erfüllt, ein Baum ist. Das ist ein großer Unterschied. Bitte immer genau lesen. ─ cauchy 05.10.2023 um 12:16
"Biimplikation" ist (für mich) eine ungewöhnliche Bezeichnung, scheint aber von manchen verwendet zu werden-
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mikn
05.10.2023 um 12:19
Okay. Konnte ich nichts zu finden.
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cauchy
05.10.2023 um 12:21
Wir haben gelernt das genau dann wenn, eine Biimplikation bedeutet. Ich verstehe halt nicht was mit der Induktion gezeigt werden soll. Mein Bsp. war falsch, ich meinte einen Graphen der die Teilgraphen $K_3$ und $K_2$ hat, da gibt es ja 5 Knoten und 4 kanten. Und wir nennen das Biimplikation im Studium.
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henry dutter
05.10.2023 um 14:33
Folge den Hinweisen, damit Hilfe ansetzen kann. Falls notwendig, Induktion wiederholen. Aussagen sorgfältig und vollständig notieren.
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mikn
05.10.2023 um 15:09
Ich habe, wie bereits gesagt, es so verstanden, das wenn die Summe gilt, es ein Baum sein muss und er mit der Induktion das gezeigt werden soll. Dazu habe ich ja ein gegenbeispiel gezeigt mit dem Graph der die Komponenten $K_3$ und $K_2$ hat (Der sieht ja eindeutig aus). Aber mir wurde ja hier gesagt, das es da nicht steht, deshalb wollte ich fragen was sonst mit der Induktion gezeigt werden soll.
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henry dutter
05.10.2023 um 16:09
Ein Beispiel wäre ein guter Einstieg, aber bis jetzt hast du das noch nicht vorgelegt (Hinweise dazu oben). Und "mir wurde gesagt..." heißt, du hast es selbst noch nicht verstanden. Da könnte das Beispiel helfen... genug Tipps gegeben...
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mikn
05.10.2023 um 16:40
Also, am besten, man schreibt sich die "\(\Leftarrow\)"-Richtung mal sauber, als eigenen Satz formuliert, auf:
Satz:
Sei \(d_1,\ldots,d_n \in \mathbb{N}\) eine Folge positiver, natürlicher Zahlen.
Sei \(\displaystyle \sum_{i=1}^n d_i = 2n-2\).
Dann gibt es einen Baum mit der Knotenmenge \( \{v_1,\ldots,v_n\}\) und \(\mbox{deg}(v_i)=d_i\).
Dass es da noch andere Nicht-Baum-Graphen mit n Knoten und \(\mbox{deg}(v_i)=d_i\) gibt, ist egal. Diese Nicht-Baum-Graphen interessieren nicht, denn nichts davon steht im obigen Satz. Im Satz geht es nur um Bäume.
─ m.simon.539 05.10.2023 um 18:50
Satz:
Sei \(d_1,\ldots,d_n \in \mathbb{N}\) eine Folge positiver, natürlicher Zahlen.
Sei \(\displaystyle \sum_{i=1}^n d_i = 2n-2\).
Dann gibt es einen Baum mit der Knotenmenge \( \{v_1,\ldots,v_n\}\) und \(\mbox{deg}(v_i)=d_i\).
Dass es da noch andere Nicht-Baum-Graphen mit n Knoten und \(\mbox{deg}(v_i)=d_i\) gibt, ist egal. Diese Nicht-Baum-Graphen interessieren nicht, denn nichts davon steht im obigen Satz. Im Satz geht es nur um Bäume.
─ m.simon.539 05.10.2023 um 18:50
Entschuldigung, die zweite Implikation habe ich falsch verstanden, vielen Dank. Versuch mich jetzt noch mal an die Induktion heran.
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henry dutter
05.10.2023 um 19:22
@simon Meine Idee war, dass der Frager sich erstmal selbst mit der Aussage auseinandersetzt. Dieses Vorlesen-aus-Büchern und das Denken abnehmen bringt doch nichts. Und es war nun klar was passiert: Er setzt sich nicht mehr mit seinem Beispiel und der Aussage auseinander, wozu auch? Also gleich ran an die Induktion. Schade, Chance vertan.
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mikn
05.10.2023 um 19:46
@Mikn: Naja, wenn man's anders macht, bleibt's halt nebulös.
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m.simon.539
05.10.2023 um 20:25
@simon Man sollte als Helfer auch abwarten können. Und ob es nun weniger nebulös ist, werden wir ja sehen.
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mikn
05.10.2023 um 20:34