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Unformatted text preview: D 7 E 12 A B~:jy ~D @ Minimum sum of weights of two incident edges 4 9 5 12 3 Sum 15 19 16 19 15 As the table shows, any Hamiltonian cycle must have weight at least 19. The Hamiltonian cycle AECBDA has weight 1 + 2 + 4 + 5 + 7 = 19 and hence is a minimum. 15. (a) [BB] The graph is complete, so an obvious approach is to try to choose the lowest weight available edge at each vertex. One such cycle is ADEFBCA, which has weight 2+3+2+5+ 1+5 = 18. (b) [BB] As shown on the left, the minimum weight of a spanning tree after A is removed is 11. The two edges of least weight at A have weights 2 and 3 so we obtain an estimate of 11 + 2 + 3 = 16 as a lower bound for the weight of any Hamiltonian cycle....
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- Summer '10
- Graph Theory