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 B.4, Problem 2E
Program Plan Intro
To determine if the directed or the undirected graph comprises a path among
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A simple directed graph with vertices A,B,C,D,E,F,G has adjacency matrix
Say that a graph G has a path of length three if there exist distinct vertices u, v, w, t with edges (u, v), (v, w), (w, t). Show that a graph G with 99 vertices and no path of length three has at most 99 edges.
Let G be a connected graph that has exactly 4 vertices of odd degree: v1,v2,v3 and v4.
Show that there are paths with no repeated edges from v1 to v2, and from v3 to v4, such that every edge in G is in exactly one of these paths.
Chapter B Solutions
Introduction to Algorithms
Ch. B.1 - Prob. 1ECh. B.1 - Prob. 2ECh. B.1 - Prob. 3ECh. B.1 - Prob. 4ECh. B.1 - Prob. 5ECh. B.1 - Prob. 6ECh. B.2 - Prob. 1ECh. B.2 - Prob. 2ECh. B.2 - Prob. 3ECh. B.2 - Prob. 4E
Ch. B.2 - Prob. 5ECh. B.3 - Prob. 1ECh. B.3 - Prob. 2ECh. B.3 - Prob. 3ECh. B.3 - Prob. 4ECh. B.4 - Prob. 1ECh. B.4 - Prob. 2ECh. B.4 - Prob. 3ECh. B.4 - Prob. 4ECh. B.4 - Prob. 5ECh. B.4 - Prob. 6ECh. B.5 - Prob. 1ECh. B.5 - Prob. 2ECh. B.5 - Prob. 3ECh. B.5 - Prob. 4ECh. B.5 - Prob. 5ECh. B.5 - Prob. 6ECh. B.5 - Prob. 7ECh. B - Prob. 1PCh. B - Prob. 2PCh. B - Prob. 3P
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- Prove 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_forwardProve the following claim : Given a graph G and two vertices a,b of it, there is a walk between a and b if and only if there is a trail between a and b if and only if there is a (simple) path between a and b.arrow_forwardGive an example of a graph (with or without weights on the edges) where the betweenness and closeness centrality points are different. The graph must be composed of at least 5 vertices and at most 8 vertices.arrow_forward
- (a) Show that a graph G with at least three vertices is 2-connected if and only if any vertex and any edge of G lie on a common cycle of G: (b) Show that a graph G with at least three vertices is 2-connected if and only if any two edges of G lie on a common cyclearrow_forwardHow many edges does a graph have if its degree sequence is 2, 4, 4, 5, 3?A. Draw a graph with the above listed sequence.B. Is it possible to draw an Euler Circuit with such a sequence of vertex degrees?Is it possible to draw an Euler Path? If yes, to either of these questions, draw the a graph that supports your answer.arrow_forwardDraw the following:a. Complete graph with 4 vertices b. Cycle with 3 vertices c. Simple graph with 2 vertices d. simple disconnected graph with 3 vertices e. graph that is not simple. For each of the graphs shown below, determine if it is Hamiltonian and/or Eulerian. If the graph is Hamiltonian, find a Hamilton cycle; if the graph is Eulerian, find an Euler tour.arrow_forward
- Using EXACTLY three nodes and three edges per graph, draw thefollowing graphs: (a) unweighted and undirected, (b) a DAG, (c) directed and connected, and (d)weighted, directed, and disconnected.arrow_forwardconstruct a graph with vertices E,F,G,H,I whose degrees are 2,2,3,3,4 what is the edge set?arrow_forwardThe graph with edges AB, BC, CD and DA is a complete graph. True or Falsearrow_forward
- Prove or disprove that a graph is bipartite if and only if every induced cycle has even length.arrow_forwardConsider an undirected graph with 100 nodes. Give the maximum number of edges the graph can contain if the graph is not connected.arrow_forwardDoes there exist a simple graph with five vertices of the following degree? If so, draw such a graph. 0, 1, 2, 2, 3arrow_forward
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