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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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This note was uploaded on 11/26/2011 for the course MATH 239 taught by Professor M.pei during the Spring '09 term at Waterloo.
- Spring '09