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Unformatted text preview: which the greedy coloring uses only χ ( G ) colors. (b) (5 points) Demonstrate that for any k > 2 there is a bipartite graph G on 2 k vertices and vertex ordering thereon in which the greedy coloring uses k colors, even though χ ( G ) = 2. (c) (5 points) Show that a greedy coloring of the cycle C n , regardless of the value of n , does not use more than 3 colors. 4. (5 points) Prove that a bipartite graph on n > 2 vertices is planar only if it has 2 n-4 or fewer edges. 5. (5 point bonus) Prove that for every value of k > 2, there is a tree and ordering of the vertices thereon such that a greedy coloring (see above) of the tree requires k colors. What is the smallest such tree you can ﬁnd? Page 1 of 1 Due March 23, 2010...
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This note was uploaded on 01/12/2012 for the course MATH 682 taught by Professor Wildstrom during the Spring '09 term at University of Louisville.
- Spring '09