Question: following was your answer 1. Cycle: A-B-C-A Edges: A - B(x), B - C(3), C - A(5) . The heaviest in this cycle will not

following was your answer

1. Cycle: A-B-C-A Edges: A - B(x), B - C(3), C - A(5) . The heaviest in this cycle will not be included in an MST. . If 5, A - B is the heaviest and will never be chosen in this cycle. 2. Cycle: A-B-C-D-A Edges: A - B(x), B - C(3), C - D(1), D - A(4) . The maximum weight in this cycle: max(x, 1, 3, 4). . If x 4, A - B is the heaviest. 3. Cycle: A-B-C-D-E-A Edges: A - B(x), B - C(3), C - D(1), D - E(2), E - A(2) . The maximum: max(x, 1, 2, 2, 3). . If ax 3, A - B is the heaviest. In all cycles, the strictest condition comes from this last (longest) cycle: . If a 5, then A - B is the heaviest in the 3-cycle and is never included in any MST. . But lower values are even stricter in the other cycles. So, let's check the smallest such value. . In A - B - C - D - E - A, x 3 is the strictest; if a 3, then A - B is heaviest in this cycle and not used in any MST

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