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could you explain how Kruskal's algorithm works on here

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Why divide by 5 and not 4?

Why does it differ from Q7?

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Could I just state "BFS algorithm", give it's run time and state if an odd cycle is returned then its confirmed to not be bipartite? Basically, if i give the solution in simple manner would I still be correct?

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Why does the union operation take O(log |X|) time?

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Why does the union operation take O(log |X|) time?

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Could you go through this question. I understand that running a DFS means the walk visits the edge exactly twice but I can't go on from there