Find the upper bound of the minimum number of spanning trees needed to cover all links in the graph
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Please I need the answer from the expert  in the graph theory or any one know it.

My question:

If we have graph G(V,E), where V is set of nodes and E is set of links, 
what is the minimum number of spanning trees needed to cover all the links in the graph.

for example:
In G(V,E) we have five links (1,2,3,4,5)
after generale all eight spanning trees in lexicographic order for the G as the following: 
1 2 4
1 2 5
1 3 4
1 3 5
1 4 5
2 3 4
2 3 5
2 4 5

In this case, the minimum number of spanning trees needed to cover all the links in the graph
will be 3 spanning trees ({1 2 4},{1 2 5 },{1 3 4}). So all the links are included in these 3 spanning trees.

It easy to know how many spanning trees are needed to cover all links in the graph for very small graph, but what about the large size graph?

Is there any formula to compute the upper bound number for the spanning trees to cover all links in the graph.


thanks alot


				


