A bridge is an edge whose removal disconnects the graph. Prove that any bridge must be...
A bridge is an edge whose removal disconnects the graph. Prove that any bridge must be in some minimum spanning tree. You may use the cut property in the proof, if you want.
Homework Answers
Explanation:
---------------
As we know,To get a minimum spanning tree we need to eliminate E-V+2 edges in the graph.
While removing we need to eliminate highest cost edge or pick lowest cost edge.
So while finding through kruskal algorithm,we need to be aware of not getting cycles.
If using prim's algorithm,Choose lowest cost edge and continue.
A edge should never be removed ,if it is the only edge connecting to remaining path.
Even if the cost edge is more ,since it is the only edge to reach next path.So we need to consider it.
And this is called a Bridge.
Since we know spanning tree is a minimal path connecting all vertices.
so if there is only one edge in the path,we cant eliminate it.
And this is called a bridge.
Hope this helps!
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