Question - Is there anybody who knows how to do this problem? This is part of a homework assignment that I am working on and I really need help! Here's how it works:
Consider that a graph has distinct edge weights. Does its lightest edge have to belong to the MST (Minimum Spanning Tree)?
Will its heaviest edge belong to the MST? Does a min-weight edge on every cycle have to belong to the MST?
Prove your answer to each question or provide a counterexample. Your proofs do not need to be excessively formal. A convincing argument is adequate. Is there anybody who knows how to do this?