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 35.1, Problem 3E
Program Plan Intro
To show that the professor’s heuristic does not have an approximation ratio of 2.
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Demonstrate how an Approximation approach can be utilised to solve the Vertex Cover problem for the following graph.
a. Show that if G is a simple graph with n vertices (wheren is a positive integer) and each vertex has degree greater than orequal to (n−1)/2, then the diameter of G is 2 or less.
b. If G is a (not necessarily simple) graph with n verticeswhere each vertex has degree greater than or equal to (n−1)/2, is thediameter of G necessarily 2 or less? Either prove that the answer tothis question is "yes" or give a counterexample.
Part a has already been answered so I only need help with part b. Part a is included for context
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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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- 1. Let F be a forest with n vertices and k connected components, with 1 < k < n. (a) Compute ) deg(v) in terms of n and k. vɛV(F) (b) Show that the average degree of a vertex in F is strictly less than 2. (c) Conclude that forests have leaves.arrow_forwardConsider two graphs G and H. Graph G is a complete graph with 5 vertices; Graph H is a 2-regular graph with 10 vertices. How many edges are there in total between the two graphs?arrow_forwardLet G be a polyhedral graph with 12 vertices and 30 edges. Prove that the degree of each face of G is three. Show all of your work and clearly explain, using words, your reasoning.arrow_forward
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