Question: Please explain step by step, it's important for my exam, thanks. 7. A cutset in a connected graph G is a set K of edges

Please explain step by step, it's important for my exam, thanks.

Please explain step by step, it's important for my exam, thanks. 7.

7. A cutset in a connected graph G is a set K of edges whose removal disconnects G, but the removal of any proper subset of K does not disconnect G. For example, in the graph in problem 7, the set K-(a), (b.g). (c h), (di), (ej)) is a cutset separating (a.b.cd.c) from the rest of the vertices, while no proper subset of these 5 edges disconnects the graph a) Find a cutset in the right graph in problem 1 with 4 edges b) Explain briefly why any spanning tree of a connected graph G must intersect any cutset of G c) If Kis a cutset in a connect graph G and C is a circuit in G, explain briefly why K and C must have an even number of edges in common (possibly zero). 7. A cutset in a connected graph G is a set K of edges whose removal disconnects G, but the removal of any proper subset of K does not disconnect G. For example, in the graph in problem 7, the set K-(a), (b.g). (c h), (di), (ej)) is a cutset separating (a.b.cd.c) from the rest of the vertices, while no proper subset of these 5 edges disconnects the graph a) Find a cutset in the right graph in problem 1 with 4 edges b) Explain briefly why any spanning tree of a connected graph G must intersect any cutset of G c) If Kis a cutset in a connect graph G and C is a circuit in G, explain briefly why K and C must have an even number of edges in common (possibly zero)

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