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 6E
Program Plan Intro
To determine that we can depict a hyper-graph by using the bipartite-graph as long as we assume incidence in hyper-graph correlate to contiguousness in bipartite-graph.
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Prove that "If a connected planar simple graph has e edges and v vertices with v ≥ 3 and no circuits of length three, then e ≤ 2v − 4."
Determine whether or not the loop-free undirected graphs with the following adjacency matrices are isomorphic. Explain why.
Give a condition that is sufficient, but not necessary, for an undirected graph to not have an Eulerian cycle. Justify what you are saying.
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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- (a) Draw a connected 3-regular graph with 6 vertices and no loops (b) Show that every 3-regular graph must have an even number of vertices. (c) Find two non-isomorphic connected 3-regular graphs with 6 vertices.arrow_forwardDetermine whether graphs G and H are planar or not. To show planarity, give aplanar embedding. To show that a graph is not planar, use Kuratowski’s theoremarrow_forwardSay 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.arrow_forward
- Let A and B each be sets of N labeled vertices, and consider bipartite graphs between A and B. What is the maximum number of edges possible for any bipartite graph between A and B?arrow_forwardDetermine if a graph with the property specified below exists. If it exists, draw the graph and give its adjacency matrix; otherwise, prove that the graph doesn't exist. (a) A simple digraph with in-degrees 0, 1, 2, 2 and out-degrees 0, 1, 1, 3. (b) A simple digraph with in-degrees 0, 1, 1, 2 and out-degrees 0, 1, 1, 1.arrow_forwardPlease solve with the computer Question 2: Draw a simple undirected graph G that has 11 vertices, 7 edges.arrow_forward
- Give a condition that is sufficient, but not necessary, for an undirected graph to not have an Eulerian cycle. Please explain your stance.arrow_forwardGiven the adjacency matrix of an undirected simple graph G = (V, E) mapped in a natural fashion onto a mesh of size n2, in Ο(n) time it can be decided whether or not G is bipartite prove it.arrow_forwardGive a condition that is sufficient, but not necessary, for an undirected graph to not have an Eulerian cycle. Justify what you're saying.arrow_forward
- Show that an MST of an undirected graph is equivalent to abottleneck SPT of the graph: For every pair of vertices v and w, it gives the path connecting them whose longest edge is as short as possible.arrow_forwardGive a condition that is necessary but not sufficient for an undirected graph to have an Eulerian Path. Justify your answer.arrow_forwardGive a condition that is sufficient but not necessary for a graph to be undirected and without an Eulerian cycle. Justify what you're saying.arrow_forward
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