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Unformatted text preview: AMS 301 Exam 1 Solution Ning SUN July 30, 2009 1 True or False. 1. False. K 1 , 6 is planar, but we need 6 colors to color its edges, since there is a vertex of degree 6. 2. False. K 3 , 3 is a counterexample. 3. True. The number of edges of any spanning tree is n 1 , where n is the number of vertices in the graph. 2 Isomorphic? The graphs are NOT isomorphic. • The graphs have the same number of vertices, 8, and all have degree 3. • Graph on right is bipartite: { A,H,C,F } { B,D,E,G }, graph on left is not (an odd circuit is 184761). • Also the right one is planar (it's already in a planar depiction), but the left one is not . Here I use the circlechord method to show the K 3 , 3 con guration of the left graph. 3 Modeling the problem as a graph coloring problem 1. V : teams. 2. E : 2 vertices have an edge connecting them if the corresponding teams have students in common. 3. being colored: Vertices....
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 Spring '08
 ARKIN
 Graph Theory, Planar graph, vertices, Hamilton circuit

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