45. In a mathematical competition some competitors are friends. Friendship is always mutual. Call a group of competitors a clique if each two of them are friends. (In particular, any group of fewer than two competitors is a clique.) The number of members of a clique is called its size. Given that, in this competition, the largest size of a clique is even, prove that the competitors can be arranged in two rooms such that the largest size of a clique contained in one room is the same as the largest size of a clique contained in the other room.

Open in App

Solution

Suggest Corrections

Similar questions

Q. Suppose a polynomial time algorithm is discovered that correctly computes the largest clique in a given graph. In this scenario, which one of the following represents the correct Venn diagram of the complexity classes P, NP and NP Complete (NPC)?

Q. In an essay competition, tho odds is favour of competitors

P, Q, R, S

are

1 : 2, 1 : 3, 1 : 4

, and

1 : 5

respectively. Find the probability that one of them wins the competition.

In a shooting competition the scores of a competitor were as given below:

Q. The students of a Vidyalaya were asked to participate in a competition for making and decorating penholders in the shape of a cylinder with a base, using cardboard. Each penholder was to be of radius

3 c m

and height

10.5 c m

. The Vidyalaya was to supply the competitors with cardboard. If there were

35

competitors, how much cardboard was required to be bought for the competition?

The students of a Vidyalaya were asked to participate in a competition for making and decorating pen holders in the shape of a cylinder with a base, using cardboard. Each pen holder was to be of radius $3 c m$ and height $10.5 c m$ . The Vidyalaya was to supply to the competitors with cardboard. If there were $35$ competitors, how much cardboard was required to be bought for the competition?

Join BYJU'S Learning Program