سوالی از IMO 2007 (ترکیبیات ممتاز)
- شروع کننده موضوع Goharshady
- تاریخ شروع
- برچسپ ها ترکیبیات سوال ممتاز
اصل سوال :
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 competitiors 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 into 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.
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 competitiors 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 into 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.
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