Prove that every loop-free connected planar graph has a vertex v with deg (u) 6.

Question:

Prove that every loop-free connected planar graph has a vertex v with deg (u) ≤ 6.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Discrete and Combinatorial Mathematics An Applied Introduction

ISBN: 978-0201726343

5th edition

Authors: Ralph P. Grimaldi

See More Books

Question Posted: Jun 21, 2016 08:48 AM

See More Questions

Let G = (V, E) be a loop-free connected planar graph. If G is isomorphic to its dual and |V| = n, what is |E|?
Suppose that a connected planar graph has six vertices, each of degree four. Into how many regions is the plane divided by a planar representation of this graph?
Prove that for each n Z+ there exists a loop-free connected undirected graph G = (V, E), where |V| = 2n and which has two vertices of degree i for every 1 i n.
At the beginning of Section 12.6, it was noted that given the CBC MAC of a oneblock message $X$, say $T=\operatorname{MAC}(K, X)$, the adversary immediately knows the CBC MAC for the two-block...
How should the fieldworker terminate the interview?
Many stakeholders described the past CEO of CMC, Don Wilson, as a visionary who helped the organization grow and prosper for more than 20 years. His successor, Ron Henderson, took the organization...
(Appendix 4A) Why are fixed assets on the balance sheet not valued at present value?
You have just landed a summer internship (congratulations) with the management information services group of Pirelli, the Italian global tire manufacturer. Management is acutely aware of the...
Gonzalez Company is considering two new projects with the following net cash flows. The company's required rate of return on investments is 10% (PV of $1. FV of $1, PVA of $1, and FVA of $1) (Use...
Using Î± = 0.05, perform a hypothesis test with the data from Problem 18.35 to determine if the population rank correlation coefficient is less than zero. From Problem Variable 4 72 6 6...
Suppose that G = (V, E) is a loop-free planar graph with | V | = v, | E | = e, and k (G) = the number of components of G. (a) State and prove an extension of Euler's Theorem for such a graph, (b)...
(a) Let G = (V,E) be a loop-free connected graph with | V | 11. Prove that either G or its complement must be nonplanar. (b) The result in part (a) is actually true for | V | 9, but the proof for |...
In a test of the XSORT method of gender selection, 574 babies are born to couples trying to have baby girls, and 525 of those babies are girls (based on data from the Genetics & IVF Institute). a. If...
Shire Company's predetermined overhead rate is based on direct labor cost. Management estimates the company will incur $649,000 of overhead costs and $590,000 of direct labor cost for the period....
You plan to live 25 years after you retire. You want to withdraw $100,000 each year for 25 years. Your first withdrawal will take place the day after you retire. What is the four annuity formulas...
Harwood Company's quality cost report is to be based on the following data: 2021 2022 Depreciation of test equipment $94,000 $95,000 Audits of the effectiveness of the quality system $54,000 $51,000...
Cash contribution of 4,000 to the Accounting Society (a charity) Purchase of art object at an Accounting Society Charitable event for $1,200 (FMV $800) Donation of 3-year-old clothing (basis 800; FMV...
The government is issuing $100 million in 10 year debt and receives the following bids. $25 million is reserved for non-competitive tenders. At what yield will the non-competitive tenders be issued...
In the managerial folklore about discipline there is a type of stereotypically problematic employee which one consultant described as the professional weeper. In other words, some people respond to...
The manager of a local convenience store is expanding his line of small toy items. To price these new items, the manager is looking at the prices being charged by competing retailers in his area. For...
Show that every square matrix A can be factored as A = RQ, where R is symmetric, positive semidefinite and Q is orthogonal. Every complex number can be written in polar form as z = rei, where r = |z|...
Find a polar decomposition of the matrices in Exercises 1-2. 1 3
In Exercises 1-2, find the best linear approximation to f on the interval [-1, l]. 1. f(x) = x2 2. f(x) = x2 + 2x
Compute the value of ordinary bonds under the following circumstances assuming that the coupon rate is 0.06:(either the correct formula(s) or the correct key strokes must be shown here to receive...
A tax-exempt municipal bond has a yield to maturity of 3.92%. An investor, who has a marginal tax rate of 40.00%, would prefer and an otherwise identical taxable corporate bond if it had a yield to...
Please note, kindly no handwriting. Q. Suppose a 3 year bond with a 6% coupon rate that was purchased for $760 and had a promised yield of 8%. Suppose that interest rates increased and the price of...

Prove that every loop-free connected planar graph has a vertex v with deg (u) 6.

Question:

Step by Step Answer:

If not degv 6 for a...View the full answer

Discrete and Combinatorial Mathematics An Applied Introduction

Students also viewed these Linear Algebra questions