g acceleration of gravity

1. It's defined as the spanning tree of G such

2. And we assume that it has the same vertices of G of course.

3. Well, of course it cover all the vertices of G

4. So we say for all G and for all sets

5. What is G?

6. that covers all the vertices of G?

7. So let this be a connected subgraph of G.

8. Do we still have a connected subgraph of G

9. with the same vertices of G. So the only difference

10. What is G?

11. there exists a minimum spanning tree of G.

12. So this is the minimum spanning tree for the graph G

13. So this is the minimum spanning tree for the graph G

14. So what I need to proof is that for all G,

15. We said that a connected graph, G-- that's

16. there exists a minimum spanning tree of G such

17. let T be a connected subgraph of G, but with a property

18. So all vertices in G are still connected

19. because we showed that for all graphs G,

20. So what I need to proof is that for all G,

21. It's defined as the spanning tree of G such

22. a connected graph G.

23. So I have to prove that for all G,

24. There does not exist a connected graph G that has no ST.

25. connected, and with the same vertices as G.

26. For all G, I still need to prove there

27. So we already know that T is a connected subgraph of G

28. Do we still have a connected subgraph of G

29. is that for any connected weighted graph G,

30. So we know a subgraph of G that touches all the different edges