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examsamples2

# examsamples2 - Here is a list of terms you will be assumed...

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Here is a list of terms you will be assumed to be familiar with, not that this list may not be complete. subset graph isomorphic connected degree (sequence) planar Find the chromatic number of the following graph. u u u u u u @ @ @ @ @ H H H H H H H H H H P P P P P P P P P P P P P P P Draw a loop-free undirected simple graph on 10 vertices with 20 edges, such that the graph is planar and has an Eulerian circuit. State why the graph drawn satisfies all these properties. Alice and Bob are examining a graph with 12 vertices and 31 edges. Alice insists that the graph is planar, but Bob disagrees. Can we tell who is correct, and if so who? Explain your answer in full detail. There are four graphs, each of which has exactly one of the following properties; one contains a cycle containing every vertex, one contains an Eulerian circuit, one is planar, and one is has multiple edges. These graphs have the following degree sequences; 7 , 7 , 7 , 7 , 7 , 7 , 6 , 6 2 , 2 , 4 , 4 , 6 , 6 , 6 , 6 4 , 4 , 4 , 4 , 4

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