Discrete Mathematics with Graph Theory (Classic Version) (3rd Edition) (Pearson Modern Classics for Advanced Mathematics Series)
3rd Edition
ISBN: 9780134689555
Author: Edgar Goodaire, Michael Parmenter
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Question
Chapter 13.2, Problem 10E
(a)
To determine
A sub graph homeomorphic to
(b)
To determine
A sub graph homeomorphic to
(c)
To determine
Whether the given graph is planar or not.
(d)
To determine
The chromatic number of the graph.
(e)
To determine
The converse of the 4-Color Theorem by using this graph.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
I tried asking this in seperate questions but no body answered . b) Prove that G = K2,12 is planar by drawing G without any edge crossings.
(c) Give an example of a graph G whose chromatic number is 3, but that contains no K3 as a subgraph. You must prove that your graph actually has chromatic number 3.
6.b. Determine whether the following statements are true or false. Explain why the true statements are true and give counterexamples to the false statements.(i) Each bipartite graph is planar.(ii) Each bipartite has a chromatic number equal to 2.
True or False:
a.) The cycle graph C4 is a subgraph of the complete graph k4? T or F
b.) The cycle graph C3 is isomorphic to the complete graph K3. T or F
Chapter 13 Solutions
Discrete Mathematics with Graph Theory (Classic Version) (3rd Edition) (Pearson Modern Classics for Advanced Mathematics Series)
Ch. 13.1 - Prob. 1TFQCh. 13.1 - Prob. 2TFQCh. 13.1 - Prob. 3TFQCh. 13.1 - Prob. 4TFQCh. 13.1 - Prob. 5TFQCh. 13.1 - Prob. 6TFQCh. 13.1 - Prob. 7TFQCh. 13.1 - Prob. 8TFQCh. 13.1 - Prob. 9TFQCh. 13.1 - Prob. 10TFQ
Ch. 13.1 - [BB] Show that the graph is planar by drawing an...Ch. 13.1 - Prob. 2ECh. 13.1 - Prob. 3ECh. 13.1 - 4. One of the two graphs is planar; the other is...Ch. 13.1 - Prob. 5ECh. 13.1 - Prob. 6ECh. 13.1 - Prob. 7ECh. 13.1 - Prob. 8ECh. 13.1 - Prob. 9ECh. 13.1 - Prob. 10ECh. 13.1 - Prob. 11ECh. 13.1 - Prob. 12ECh. 13.1 - Prob. 13ECh. 13.1 - Prob. 14ECh. 13.1 - Prob. 15ECh. 13.1 - Discover what you can about Kazimierz Kuratowski...Ch. 13.1 - Prob. 17ECh. 13.1 - Prob. 18ECh. 13.1 - Prob. 19ECh. 13.1 - [BB] Prove that every planar graph V2 vertices has...Ch. 13.1 - Prob. 21ECh. 13.1 - [BB] suppose G is a connected planar graph in...Ch. 13.1 - Prob. 23ECh. 13.1 - Prob. 24ECh. 13.1 - Prob. 25ECh. 13.2 - Prob. 1TFQCh. 13.2 - Prob. 2TFQCh. 13.2 - Prob. 3TFQCh. 13.2 - Prob. 4TFQCh. 13.2 - Prob. 5TFQCh. 13.2 - Prob. 6TFQCh. 13.2 - Prob. 7TFQCh. 13.2 - Prob. 8TFQCh. 13.2 - Prob. 9TFQCh. 13.2 - Prob. 10TFQCh. 13.2 - Prob. 1ECh. 13.2 - Prob. 2ECh. 13.2 - Prob. 3ECh. 13.2 - Prob. 4ECh. 13.2 - Prob. 5ECh. 13.2 - Prob. 6ECh. 13.2 - Prob. 7ECh. 13.2 - Prob. 8ECh. 13.2 - Prob. 9ECh. 13.2 - Prob. 10ECh. 13.2 - Prob. 11ECh. 13.2 - Prob. 12ECh. 13.2 - Prob. 13ECh. 13.2 - Prob. 14ECh. 13.2 - Prob. 15ECh. 13.2 - Prob. 16ECh. 13.2 - Prob. 17ECh. 13.2 - Prob. 18ECh. 13.2 - Prob. 19ECh. 13.2 - Prob. 20ECh. 13.2 - [BB] The following semester, all the students in...Ch. 13.2 - Prob. 22ECh. 13.2 - 23. The local day care center has a problem...Ch. 13.2 - Prob. 24ECh. 13.2 - Prob. 25ECh. 13.2 - (a) [BB] Draw the dual graph of the cube...Ch. 13.2 - [BB] is it possible for a plane graph, considered...Ch. 13.3 - Prob. 1TFQCh. 13.3 - Prob. 2TFQCh. 13.3 - Prob. 3TFQCh. 13.3 - Prob. 4TFQCh. 13.3 - Prob. 5TFQCh. 13.3 - Prob. 6TFQCh. 13.3 - Prob. 7TFQCh. 13.3 - Prob. 8TFQCh. 13.3 - Prob. 9TFQCh. 13.3 - Prob. 10TFQCh. 13.3 - Prob. 1ECh. 13.3 - Prob. 2ECh. 13.3 - [BB] True or False? A line-of-sight graph is...Ch. 13.3 - Prob. 4ECh. 13.3 - Prob. 5ECh. 13.3 - Prob. 6ECh. 13.3 - Prob. 7ECh. 13.3 - Prob. 8ECh. 13.3 - [BB] Assume that the only short circuits in a...Ch. 13.3 - Prob. 10ECh. 13.3 - 11. Find a best possible feasible relationship...Ch. 13.3 - Prob. 12ECh. 13.3 - Prob. 13ECh. 13.3 - Prob. 14ECh. 13.3 - Prob. 15ECh. 13.3 - [BB] Apply Brookss Theorem (p. 422 ) to find the...Ch. 13 - (a) Show that the graph below is planar by drawing...Ch. 13 - Prob. 2RECh. 13 - Prob. 3RECh. 13 - Prob. 4RECh. 13 - Prob. 5RECh. 13 - Prob. 6RECh. 13 - Prob. 7RECh. 13 - Prob. 8RECh. 13 - Prob. 9RECh. 13 - Prob. 10RECh. 13 - Prob. 11RECh. 13 - Prob. 12RECh. 13 - Prob. 13RECh. 13 - 14. Suppose that in one particular semester there...Ch. 13 - Prob. 15RECh. 13 - 16. Draw the line-of-sight graph associated with...Ch. 13 - Prob. 17RECh. 13 - Prob. 18RECh. 13 - Prob. 19RECh. 13 - A contractor is building a single house for a...Ch. 13 - 23. The Central Newfoundland Hospital Board would...
Knowledge Booster
Similar questions
- a If a graph is symmetric with respect to the x-axis and (a,b) is on the graph, then (,) is also on the graph. b If a graph is symmetric with respect to the y-axis and (a,b) is on the graph, then (,) is also on the graph. c If a graph is symmetric about the origin and (a,b) is on the graph, then (,) is also on the graph.arrow_forwardWhich of the following graphs contain a subdivision of K3,3 as a subgrapharrow_forward1) Sketch the graph of r=1-2cos@ 2) Sketch the graph of r=1+2sin@ 3) Sketch the graph of r=5+4cos@ 4) Sketch the graph of r=5-2sin@arrow_forward
- Sketch the graph of r=2sin3@ Sketch the graph of r=6cos3@arrow_forward(b) Suppose G is a simple connected graph with 12 vertices and 16 edges. Suppose 4 of its vertices are degree 1, and 3 of its vertices are degree 2. Prove that G is planar. (Hint: Kuratowski) (c) Let G be any simple connected planar graph with n vertices and e edges. Suppose there are exactly y vertices of degree 2. Assume that n - y > 3. Prove that e < 3n - y - 6. (Hint: Explain why the degree-2 vertices can be erased, and how to take care of any resulting loops or multiple edges.) (d) Suppose that a connected simple graph G' has exactly 10 vertices of degree 4, 8 vertices of degree 5, and all other vertices have degree 7. Find the maximum possible number of degree-7 vertices G could have, so that G would still be planar.arrow_forwardPlease explain how you arrived at your conclusion of the chromatic numbers of each of the graphs you create from the following problems. Let A be a simple graph for all the following questions. (i) Give an example of A and a subgraph B that have the same vertex set χ(B) = χ(A). (For this problem A does not equal B)(ii) Give an example of A where χ(A) > ∆(A). (In this case ∆(A) is the largest degree of a vertex in A)(iii) Give an example of A where χ(A) < δ(A). (In this case δ(A) is the smallest degree of a vertex in A)(iv) Give an example of A where χ(A) = x. (In this case x is the degree of every vertex in A)arrow_forward
- 3. (b) The degree of every vertex of a graph G is one of three consecutive integers. If, for each of the three consecutive integers x, the graph G contains exactly x vertices of degree x, prove that two-thirds of the vertices of G have odd degree. (c) Construct a simple graph with 12 vertices satisfying the property described in part (b).arrow_forwardBelow is depicted a graph ? constructed by joining two opposite vertices of ?12. Some authors call this a “theta graph” because it resembles the Greek letter ?. What are the possible total degrees of graphs obtained by identifying two vertices of ??arrow_forwardWhat is the smallest number of colors you need to properly color the vertices of K4,5? That is, find the chromatic number of the graph.arrow_forward
- on graph a any after a b carrow_forwardDefine Mycielski’s construction. Use this to obtain a graph with chromatic number4 from K2.arrow_forward(Discrete Math-Graph Theory) Let G=(V,E₁∪E₂∪E₃) be a simple graph such that G₁=(V,E₁) is planar, G₂=(V,E₂) is a forest, and G₃=(V,E₃) is a matching. Prove G is 9-colourable, i.e. its chromatic number satisfies χ(G)≤9.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Algebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:Cengage Learning