gr-t3

# B recall that your friendly n cubes are defined

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(b) Recall that your friendly n-cubes are defined recursively by Q 1 =K 2 , and for n 2, Q n =Q n-1 xK 2 . Do these friendly bipartite graphs have perfect matchings?? Explain briefly.

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TEST3/MAD3305 Page 2 of 4 _________________________________________________________________ 3. (15 pts.) (a) Show that the graph below has a strong orientation by assigning a direction to each edge so that the resulting digraph is strong. (b) The graph to the left has many strong orientations. Does the graph have an Eulerian orientation? Explain briefly. (c) If you were asked to give me an example of a connected graph which has no orientations that are strong, what feature(s) would you include in your example to ensure that the example satisfies the requirement? Why?? _________________________________________________________________ 4. (10 pts.) Theorem 5.17, a corollary of sorts to Menger’s Theorem allows you to deal with the vertex connectivity of the graph below easily. Explain briefly. [Hint: Look north-south as well as east-west after considering δ (G).]
TEST3/MAD3305 Page 3 of 4 _________________________________________________________________ 5. (15 pts.)

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b Recall that your friendly n cubes are defined recursively...

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