Critical edges.An MST edge whose deletion from the graph would cause the MST weight to inc...

Critical edges.An MST edge whose deletion from the graph would cause the MST weight to increase is called a critical edge. Show how to find all critical edges in a graph in time proportional to Elog E. Note: This question assumes that edge weights are not necessarily distinct (otherwise all edges in the MST are critical). Hint: Apply exercises 4.1.36 and show that an edge eis critical if and only if it is a bridgein the subgraph containing all edges with weight less than or equal to the weight of edge e.

Exercises4.1.36:

Two-edge connectivity.A bridgein a graph is an edge that, if removed, would increase the number of connected components. A graph that has no bridges is said to be two-edge connected.Develop a linear-time DFS-based algorithm for determining finding all bridges in a graph (and determining whether it is two-edge connected).