Unformatted text preview: cycle. 4. Show that a vertex c in the connected simple graph G is a cut vertex if and only if there are vertices u and v , both diﬀerent from c , such that every path between u and v passes through c . Note: A cut vertex is a vertex v in G such that the removal of v from G results in disconnecting the graph. 5. Prove that any tree with 2 or more nodes must have at least two leaves. Note: A leaf vertex is a node in a tree with degree 1. 6. Show that if G is a bipartite graph with v vertices and e edges, then e ≤ v 2 4 ....
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 Fall '11
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 Economics, Graph Theory, Vertex, Glossary of graph theory, Nicole Immorlica

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