Homework 3

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Write a complete proof for problem 1.4.2.5.
Hint: Let v be an arbitrary vertex with degree d and consider the edges (v,v_i) for i=1,...d, where v_i are the neighbors of v. If each of these edges are on an odd number of cycles, you should be able to argue that d is even, at which point we use a theorem from the book to conclude the graph is Eulerian.