Question: Ramseys theorem. Let G be a graph. A clique in G is a subgraph in which every two nodes are connected by an edge. An

Ramsey’s theorem. Let G be a graph. A clique in G is a subgraph in which every two nodes are connected by an edge. An anti-clique, also called an independent set, is a subgraph in which every two nodes are not connected by an edge. Show that every graph with n nodes contains either a clique or an anti-clique with at least 1/2 log₂ n nodes.

Step by Step Solution

★★★★★

3.47 Rating (157 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

A chaintype quantity index an index comparing real production in the current year to the reference c... 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 Introduction theory computation Questions!

The clique problem can be stated as follows: Given an undirected graph G = (V, E) and an integer K, does G contain a complete subgraph of at least K vertices? The vertex cover problem can be stated...

Let G be a connected, undirected graph with at least 3 vertices, and let G 3 be the graph obtained by connecting all pairs of vertices that are connected by a path in G of length at most 3. Prove...

Let G be a weighted, connected, undirected graph, and let V 1 and V 2 be a partition of the vertices of G into two disjoint nonempty sets. Furthermore, let e be an edge in the minimum spanning tree...

Consider Problem 0.14 (and its solution). Write a Java program that reads in a graph and outputs the clique from pile A and the independent set from pile B. Your program should read from standard...

Let G be a graph. A clique in G is a subgraph in which every two nodes are connected by an edge. An anti-clique, also called an independent set, is a subgraph in which every two nodes are not...

Hello! Can you give me a hand with the following questions for Computation and Complexity? 1. A clique in an undirected graph is a subgraph, wherein every two nodes are connected by an edge. A...

1. Let G = (V;E) be an undirected graph with n nodes. Recall that a subset of the nodes is called a clique if every two of them are joined by an edge. (a) Consider the following Largest Degree First1...

A clique in an undirected graph is a subgraph, wherein every two nodes are connected by an edge. A k - clique is a clique that contains k nodes. Figure below illustrates a graph with a 5 - clique. A...

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$Name:$______________________________$...

need typed answer do anyone your wish dont provide code need algorithm 2. A dominating set of a graph is a subset D of vertices such that every vertex that is not in D is adjacent to some vertex in...

A dealer professing to sell his goods at C.P., uses a 900 gm weight for a kg. his gain percent is 1. 9% 10% 3. 11% 11% 4. 5. None of these 2.

Suppose the waiting time to get food after placing an order at a fast- food restaurant is exponentially distributed with a mean of 60 seconds. If a randomly selected customer orders food at the...

What simply means unchangeable? 0 0 : 1 7 : 5 4 Multiple Choicedistributed computingledgerblockchainimmutable

Teds sister, April, was injured while performing her duties as a police officer. She was in the hospital for three weeks before she died from her wounds. The city paid directly to Ted the workers...

Functions can oft en be implemented by compilers in-line. An in-line function is when the body of the function is copied into the program space, allowing the overhead of the function call to be...

Can we use the tail-call optimization in this function? If no, explain why not. If yes, what is the difference in the number of executed instructions in f with and without the optimization?

Right before your function f from Exercise 2.34 returns, what do we know about contents of registers $t5, $s3, $ra, and $sp? Keep in mind that we know what the entire function f looks like, but for...

7. What is the implied interest rate for the first choice and which investment should you choose? 8. Suppose you want to buy some new furniture for your family room. You currently have $500 and the...

The current price of a non-dividend-paying stock is $30. Over the next six months it is expected to rise to $36 or fall to $26. Assume the risk-free rate is zero. I. What long position in the stock...

You take long position for your contract. Contract Size = 100 By using the spot and futures prices of Oct. 11, 2021 for your asset, if the continuously compounded interest rate is 10% (Use 360 days =...