Question

Suppose that H is a connected graph that contains a proper cycle. Let H′ represent the subgraph of H that results by removing a single edge from H, where the edge removed is part of the proper cycle that H contains. Argue that H′ remains connected.

Notes.

• Your argument here needs to be (slightly) different from your argument in Activity 16.3.
• Make sure you are using the technical definition of connected graph in your argument. What are you assuming about H, and what do you need to verify about H′?
• The definition of connected graph is "for every pair of vertices there exists a path between them."

Answer 1