Unformatted text preview: planar graph with at least two vertices cannot be bipartite. 6. If M and N are matchings in G and C is a cycle all of whose edges belong to M ∪ N , prove that C has even length. 7. Show that a tree has at most one perfect matching. 8. A subset S of the vertices of a graph is independent if no two vertices in it are adjacent. If G is regular with degree at least one and S is an independent set of vertices in G , prove that  S ≤ 1 2  V ( G )  ....
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 Spring '09
 M.PEI
 Math, Graph Theory, Vertex, Planar graph, Bipartite graph

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