Question: A graph G has order n=3k+3 for some positive integers k. Every vertex of G has degree k+1,k+2 or k+3.Prove that G has at least

A graph G has order n=3k+3 for some positive integers k. Every vertex of G has degree k+1,k+2 or k+3.Prove that G has at least k+3 vertices of degree k+1 or at least k+1 vertices of degree k+2 or at least k+2 vertices of degree k+3.

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

A manufacturer has acquired four small assembly plants, located in Charlotte, Tulsa, Memphis, and Buffalo. The plan is to remodel and keep two of the plants and close the other two. The table at the...

Problem 4: A Graphic Flaw 15 Find a counterexample to the following false claim, and identify the error in the proof Claim 11. For every undirected graph G- (V, E) without loops, if Vl 2 3 and every...

6 questions 1. (8 pts.) Prove that the number of edges in every simple bipartite graph on n 2 2 vertices is at most In2/4) Is this result sharp? (I.e., is there a simple bipartite graph on n vertices...

Exercises 1. (2.1.10 BM-GTM244) Show that the incidence graph of a finite projective plane has girth six. - 2. (2.1.13 BM-GTM244) Let D be a strict digraph. Setting k max{8,6), show that: a) D...

You$must$attach$this$cover$page$to$the$front$of$your$HW$or$you$will$lose$5$points.$ $ $ APMA$1860$Homework$2$ $ $ First$Name:$____________________________$$$Last$Name:$______________________________$...

seventh pages Chapter 3 Curve Sketching How much metal would be required to make a 400-mL soup can? What is the least amount of cardboard needed to build a box that holds 3000 cm3 of cereal? The...

In this question assume that p and q are atomic formulae. (a) Compare and contrast path formulae and state formulae in temporal logic. [4 marks] (b) Describe and contrast the meanings of F(G p) and...

1. A player throws a fair die and simultaneously flips a fair coin. If the coin lands heads, then she wins twice, and if tails, then one-half of the value that appears on the die. Determine her...

You have been provided with the description of a programming language, J, intended for scripting applications. Its syntax is similar to a cut-down version of Java in that it consists of function...

In a Hopfield neural network configured as an associative memory, with all of its weights trained and fixed, what three possible behaviours may occur over time in configuration space as the net...

Math\t107-6381\t-\tQuiz\t#4\t-\tSchultz\t-\tDue\tFebruary\t21,\t2016\t-\tpage\t1\tof 3 Follow\tthese\tdirections\tcarefully. This\tquiz\tis\tdue\tby\t11:59\tEastern\ttime\ton\tFebruary\t21,\t2016. o...

Alvinstar Co. is considering investing in a new animal feed project. The product will be a soup for cats to be sold in cans. Alvinstar plans to sell 100,000 cans a year for four years at a price of...

Ask the user for a positive integer. Output whether the integer is odd or even. Tell the user if the value input was not a positive integer. (Hint: %) Input a positive integer: 47 The integer is odd....

One advantage of frequency response methods is the ready availability of sinusoidal test signals for various ranges of frequencies and amplitudes. True or False

Accounting CALCULATOR FULL SCREEN PRINTER VERSION BACK NEXY Cookie Creations 4 - Natalie had a very busy December. At the end of the mon CALCULATOR PRINTER VERSION BACK NI 360 2,400 960 600 5,380...

Post the Unadjusted Trial Balance totals to the T-Accounts on the sheet labeled "T-Accounts." These numbers will represent your beginning balances. Part 2 Record the adjusting journal entries...

The unadjusted trial balance for Bramble Corp. is shown below. BRAMBLE CORP. Trial Balance October 31, 2017 Debit Credit Cash $15,540 Supplies 2,570 Prepaid Insurance 690 Equipment 4,690 Notes...

Choose an event type you are familiar with (e.g. music festival, sporting event, business event) and explain how the event could be used to generate awareness and activity in sustainability in...

Mick, Mark and Mike are directors and shareholders of MMM Hotels Pty. Ltd. Mick, the founder of the company, owns 80% of the shares while Mark and Mike each own 10% of the shares in the company. Mick...

A process contains 2 steps. The duration of Activity A is 5 minutes and it uses Resource X. The duration of Activity B is 10 minutes and it uses Resource Y. What happens to capacity if I make an...

What are the general types of interviews? Explain each.

6 How can HRM contribute to ethical management and sustainability?

3 To what extent is HRM applicable in entrepreneurial organisations?