Question: 'n 3. (30 points) Let Kn be the complete graph on n vertices; that is, its edge-set consists of all possible unordered pairs of

'n 3. (30 points) Let Kn be the complete graph on n

'n 3. (30 points) Let Kn be the complete graph on n vertices; that is, its edge-set consists of all possible unordered pairs of vertices. Suppose that some coloring of the edge-set of Kn is given. A triangle is called rainbow if it has at most one edge from each color. Show that there exists. a coloring of the edges of Kn using three colors with at least (3) rainbow triangles.

Step by Step Solution

★★★★★

3.40 Rating (153 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

To prove that there exists a coloring of the edges of Kn using three colors such that there are at l... View full answer

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 chain has at most one maximal element.

A complete graph Kn on n vertices has one edge joining every distinct pair of vertices. (a) Draw K3, K4 and K5. (b) Choose an orientation for each edge and write out the resulting incidence matrix of...

A graph is called bipartite if its vertices can be subdivided into two sets U and V such that every edge has one endpoint in U and the other endpoint in V. For example the graph in Exercise 48 is...

\fCOMPLEX VARIABLES AND APPLICATIONS Eighth Edition James Ward Brown Professor of Mathematics The University of Michigan-Dearborn Ruel V. Churchill Late Professor of Mathematics The University of...

Consider the complete graph Kn for ft 3. Color r of the vertices in Kn red and the remaining n - r ( = g) vertices green. For any two vertices v, w in Kn color the edge {u, w} (1) red if v, w are...

Could someone help me with the problems below Let d be the maximum degree of the vertices in a graph G. Prove that we can color G with d + 1 colors. Consider this statement: In any directed graph G =...

Could someone please help me with the problems below Could someone help me with the problems below Let d be the maximum degree of the vertices in a graph G. Prove that we can color G with d + 1...

Helen Caldicott raises a family and then begins a career as a caterer. As her business grows, she hires several employees and rents space near downtown that has a retail space, parking, and a garage...

Section 9.1 Reading Assignment: Solutions, Slope Fields, and Euler's Method Answer Only Exercise 1, 2, and 3 by using a screenshot provided Calculus Pearson textbook. Make sure you read these three...

Eco nomics Human lCapital Model: Fieinterpretthe human capital growth model as follows: Suppose there are two groups of people in a country, the lowskilled and the highskilled, where the lowskilled...

A 3.8% annual coupon, 14 year bond has a yield to maturity of 5.2%. Assuming the par value is $1,000 and the YTM is expected not to change over the next year, what is the expected Current Yield for...

The properties of unidirectional fiber reinforced polymer composite laminate are given as: Elasticity modulus E (GPa) Shear modulus G(GPa) Fiber (E1f)=252 (E2f)=30 25 0.32 Matrix 3,8 2 0.28 Poisson's...

Graph the function. y= se2x To draw the graph, plot three consecutive asymptotes and two points, one on each side of the second asymptote. Then click on the graph icon.

Which circuit below is a direct implementation of the propositional logic statement ~ (p V qV ~ (r^ ~ ))^\\ ~ r? Version 1 P 13 P output 9 Version 2 output R

Golebiewski Corporation has provided the following contribution format income statement. Assume that the following information is within the relevant range. Sales (5,000 units) $150,000 Variable...

Find the stable reactor period for the zero-power reactor whose no response is shown in Figure 1.35 1.3 1.25 1.2 1.15 1.1 1.05 1 0 0.25 0.5 0.75 Time (s) 1 1.25 1.5

Exercise 3.16 Account Analysis Method Shirrell Blackthorn is the accountant for several pizza restaurants based in a tri-city area. The resident of the chain wanted some help with budgeting and cost...

Avatar Financials, Inc., located on Madison Avenue, New York City, is a company that provides financial advice to individuals and small- to mid-sized businesses. Its primary operations are in wealth...

In Exercise 1-3, let 1. Compute the Euclidean norm, the sum norm, and the max norm of u. 2. Compute the Euclidean norm, the sum norm, and the max norm of v. 3. Compute d ( u, v) relative to the...

Show that the matrices U and V in the SVD are not uniquely determined.

(a) In Example 2.35, suppose all the lights are initially off. Can we push the switches in some order so that only the second and fourth lights will be on? (b) Can we push the switches in some order...

9.3. Anthropologists often try to reconstruct information using partial human remains at burialsites. For instance, after finding a femur (thighbone), they may want to predict how tall an individual...

In Example 10.11, subtract from each observation in the ith sample to obtain a set of 18 residuals. Then construct a normal probability plot and comment on the plausibility of the normality...

9.13. A report summarizing the results of a study on the relationship between a verbal aptitude test x and a mathematics aptitude test y states that x - 480. y - 500,% - 80, Sy - 120, and r - 0.60....