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Question: consider an arbitrary connected graph g with n nodes what...

Question details

Consider an arbitrary connected graph 𝐺G with 𝑛n nodes. What is the minimal number of edges do we have to add to 𝐺G in order to guarantee that there exists a Hamiltonian cycle?
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Now suppose 𝐺G has a simple path without repetition of vertices with 𝑛n nodes. How many edges do you need to add?
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