6. Prove that the number of vertices in an undirected graph with odd degree must be even. Hint. Prove by induction on the number of edges.

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6. Prove that the number of vertices in an undirected graph with odd degree must be
even. Hint. Prove by induction on the number of edges.
7. Suppose you had to color the edges of an undirected graph so that for each vertex, the
edges that it is connected to have different colors. How can this problem be
transformed into a vertex coloring problem?
Transcribed Image Text:6. Prove that the number of vertices in an undirected graph with odd degree must be even. Hint. Prove by induction on the number of edges. 7. Suppose you had to color the edges of an undirected graph so that for each vertex, the edges that it is connected to have different colors. How can this problem be transformed into a vertex coloring problem?
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