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a5 - tree can have fewer vertices of degree 1 and by...

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MATH 239 Assignment 5 This assignment is due at noon on Friday, July 6, 2007, in the drop boxes opposite the Tutorial Centre, MC 4067. 1. Prove that every tree is bipartite. Prove this result directly, without invoking Theorem 5.2.4. 2. What is the smallest number of vertices of degree 1 in a tree with 2 vertices of degree 2, 4 vertices of degree 3, and 1 vertex of degree 5? Justify your answer by proving that no such
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Unformatted text preview: tree can have fewer vertices of degree 1, and by drawing a tree that has this minimum number of vertices of degree 1. 3. The odd graph O n is the the graph whose vertices are the n element subsets of { 1 , 2 , . . . , 2 n +1 } ; two subsets (vertices) are adjacent in O n if they are disjoint. Prove that O n is connected. 1...
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