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Trees



Figure 22:





If is a 3-regular graph, then . Figure shows two spanning trees without common edges (their edges are shown, respectively, as red and blue) in a complete graph with 4 vertices. Suppose is a graph with and all vertices of degree 3.

Problem 20:

Can , as described above, have two spanning trees without common edges?

Problem 21:

Does your conclusion hold for the 3-regular graph on 4 vertices?

Answer

 
 
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