Assn10Soln - tree). The remaining weights can be assigned...

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1. Chapter 12.2, exercises 1, 7 and 8. 12.2.1: a) f, h, k, p, q, s and t b) a c) d d) e, f, j, q, s and t e) q and t f) 2 g) k, p, q, s and t 12.2.7: a b g c d h e f a) (i) and (iii) h e f a d c g b a) (ii) a b c d h e f g h g f e a d c b a b c d h g f e b) (i) b) (ii) b) (iii)
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12.2.8: a b c d e g h f a) (i) and (iii) h e d f a c b g a) (ii) a b d e c f h g b) (i) and (iii) h g e d f c a b b) (ii) 2. Chapter 13.1, exercises 2 and 3. 13.1.2: a) the distance to a is 0, to g is 10, to b is 13, to i is 14, to h is 15, to f is 21 and to c is 22. b) agbc, agif and agi 13.1.3: a) the distance to a is 0, to b is 5, to c is 6, to f is 12, to h is 12 and to g is 16. b) acf, abhg and abh
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3. Chapter 13.2, exercises 1, 2, 3 and 9. 13.2.1: The weight of the minimum spanning tree is 18. Depending on your choice of ordering of the edges (with the same weight), you may get several diFerent trees, one possibility is 2 2 3 2 2 3 1 3 a b c d e f g h i 13.2.2: a) one possibility is to assign the weights 1, 1, 2 and 2 to the spokes of the wheel (they then form the unique minimal spanning
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Unformatted text preview: tree). The remaining weights can be assigned arbitrarily. b) assign the weights 1, 1, 2 and 2 to the rim, and the remaining weights arbitrarily. A minimal spanning tree will contain exactly one of the edges with weight 2, and both choices will give at least one minimal spanning tree. 13.2.3: Not necessarily. Consider for instance a cycle of length 4 with edge weights 1, 1, 1 and 2, and let u and v be the vertices joined by the edge of weight 2. The minimum spanning tree is the path of three edges of weight 1 from u to v (weight 3), the path of minimum weight between u and v consists of the edge uv (weight 2). 13.2.9: The proof of the correctness of Kruskals theorem implies that in this case, any spanning tree other than the one found by the algorithm has strictly larger weight....
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This note was uploaded on 07/15/2010 for the course MACM 201 taught by Professor Marnimishna during the Spring '09 term at Simon Fraser.

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Assn10Soln - tree). The remaining weights can be assigned...

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