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Unformatted text preview: AMS 301.3 (Fall, 2007) Estie Arkin Exam 1 – Solution sketch Mean 79.77, median 79, high 100 (5 of them!), low 33. 1. (14 points) Are the two graphs shown below isomorphic? If so, give the isomorphism; if not, give careful reasons for your answer. No. Graph on left is bipartite, graph on right is not (an odd circuit is 123451). Also, graph on left is planar, graph on right is not. Note that both graphs have circuits of length 4, so an incorrect reason is  graph on left has circuits of length 4 but of graph on right does not (it does, such as 12561). 2. (14 points) Compute the chromatic number (vertex colouring number) of the graph G shown below. Justify your answer! (Show a colouring with χ ( G ) colours (label each node with its colour), and argue that fewer colours cannot suffice.) A B C D E F G H I J K Example in class (text page 69) shows that 4 colours are needed for the subgraph on nodes F,G,H,I,J,K (wheel). In fact 4 colours are enough for the entire graph: Colour 1 at nodes A,C,G,J, colour 2 at nodes B,D,H, colour 3 at nodes E,I, and colour 4 at K....
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This note was uploaded on 08/08/2010 for the course AMS 301 taught by Professor Arkin during the Spring '08 term at SUNY Stony Brook.
 Spring '08
 ARKIN

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