Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
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Chapter 35.2, Problem 1E
Program Plan Intro
To prove that
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Let G be a connected graph that has exactly 4 vertices of odd degree: v1,v2,v3 and v4.
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Chapter 35 Solutions
Introduction to Algorithms
Ch. 35.1 - Prob. 1ECh. 35.1 - Prob. 2ECh. 35.1 - Prob. 3ECh. 35.1 - Prob. 4ECh. 35.1 - Prob. 5ECh. 35.2 - Prob. 1ECh. 35.2 - Prob. 2ECh. 35.2 - Prob. 3ECh. 35.2 - Prob. 4ECh. 35.2 - Prob. 5E
Ch. 35.3 - Prob. 1ECh. 35.3 - Prob. 2ECh. 35.3 - Prob. 3ECh. 35.3 - Prob. 4ECh. 35.3 - Prob. 5ECh. 35.4 - Prob. 1ECh. 35.4 - Prob. 2ECh. 35.4 - Prob. 3ECh. 35.4 - Prob. 4ECh. 35.5 - Prob. 1ECh. 35.5 - Prob. 2ECh. 35.5 - Prob. 3ECh. 35.5 - Prob. 4ECh. 35.5 - Prob. 5ECh. 35 - Prob. 1PCh. 35 - Prob. 2PCh. 35 - Prob. 3PCh. 35 - Prob. 4PCh. 35 - Prob. 5PCh. 35 - Prob. 6PCh. 35 - Prob. 7P
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- Let G be the (3, 4)-complete bipartite graph.(a) List all non-isomorphic subgraphs with 5 vertices of G.(b) List all non-isomorphic induced subgraphs of G.arrow_forwardLet G = (V, E) be a connected graph that has two distinct spanning trees. Prove that |E| > |V] – 1.arrow_forwardLet G be a directed acyclic graph with exactly one source r such that for any other vertex v there exists a unique directed path from r to v. Let Gu be the undirected graph obtained by erasing the direction on each edge of G. Prove that (Gu,r) is a rooted tree.arrow_forward
- Consider a graph G that has k vertices and k −2 connected components,for k ≥ 4. What is the maximum possible number of edges in G? Proveyour answer.arrow_forwardIf a graph G = (V, E), |V | > 1 has N strongly connected components, and an edge E(u, v) is removed, what are the upper and lower bounds on the number of strongly connected components in the resulting graph? Give an example of each boundary case.arrow_forwardLet H be a planar graph with n vertices and m edges, where n >= 5. Prove that if H does not have any cycles of length 3 and 4 then 3m <= 5n - 10.arrow_forward
- Consider a connected, undirected graph G with n vertices and m edges. The graph G has a unique cycle of length k (3 <= k <= n). Prove that the graph G must contain at least k vertices of degree 2.arrow_forwardProve that if G is a connected graph, then there always is a closed walk that passes through each edge at least once and at most twice.arrow_forwardHall's theorem Let d be a positive integer. We say that a graph is d-regular if every node has degree exactly d. Show that every d-regular bipartite graph G = (L ∪ R, E) with bipartition classes L and R has |L| = |R|. Show that every d-regular bipartite graph has a perfect matching by (directly) arguing that a minimum cut of the corresponding flow network has capacity |L|arrow_forward
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