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g
acceleration of gravity
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1. connected, and with the same vertices as
G
.
2. So I have to prove that for all
G
,
3. because we showed that for all graphs
G
,
4. there exists a minimum spanning tree of
G
.
5. So what I need to proof is that for all
G
,
6. with the same vertices of
G
. So the only difference
7. And we assume that it has the same vertices of
G
of course.
8. We said that a connected graph,
G
-- that's
9. Do we still have a connected subgraph of
G
10. So what I need to proof is that for all
G
,
11. So we know a subgraph of
G
that touches all the different edges
12. So we say for all
G
and for all sets
13. So this is the minimum spanning tree for the graph
G
14. a connected graph
G
.
15. So let this be a connected subgraph of
G
.
16. It's defined as the spanning tree of
G
such
17. that covers all the vertices of
G
?
18. Well, of course it cover all the vertices of
G
19. There does not exist a connected graph
G
that has no ST.
20. So this is the minimum spanning tree for the graph
G
21. let T be a connected subgraph of
G
, but with a property
22. there exists a minimum spanning tree of
G
such
23. So all vertices in
G
are still connected
24. What is
G
?
25. is that for any connected weighted graph
G
,
26. What is
G
?
27. For all
G
, I still need to prove there
28. So we already know that T is a connected subgraph of
G
29. It's defined as the spanning tree of
G
such
30. Do we still have a connected subgraph of
G
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