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Unformatted text preview: r < s and the result is true for all such r. The vertex with label k + s was labeled from a vertex k + r, 0 ::::; r < s. If r = 0, the backtracking goes k + s --+ k --+ i. If r > 0, the backtracking goes k + s --+ k + r --+ k (by the induction hypothesis) --+ l. In either case,ik is used twice. (b) Solution 1. Vertex k gets labeled from i. By part (a), edge ik is used twice by the algorithm, once when k is labeled and once on a backtracking. Solution 2. The result is clear for k = I, so assume k > 1 and the result is true for all i, 1 ::::; i < k. Now k received its label from i, with 1 ::::; i < k and the algorithm backtracks to i (by the induction hypothesis). Since ki must be the last edge on such a backtracking k also appears in this backtracking. 15. (a) [BB] Orient the depth first search spanning tree as in 12.6.4. (b) [BB] This follows from the definitions. Chapter 12 Review 1. There are 22 such subsequences in all. start...
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This note was uploaded on 11/08/2010 for the course MATH discrete m taught by Professor Any during the Summer '10 term at FSU.
- Summer '10
- Graph Theory