Prove or disprove the statement: Suppose that u, v are the only vertices of odd degree in a simple graph G. Then, G contains a path between u and v.
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If a graph has an Eulerian circuit, then all vertices have even degree. Show more…
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Let G be a connected graph. For all vertices u and v in G, we define the distance d(u,v) to be the least number d such that there is a path between u and v of length d. Prove that for all vertices u, v and w, d(u,w) ≤ d(u,v) + d(v,w).
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