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Minimum number of K_3 under some constraints.

Source: 2018 China Southeast MO Grade 10 P7

July 31, 2018
combinatoricsgraph theory

Problem Statement

There are 2424 participants attended a meeting. Each two of them shook hands once or not. A total of 216216 handshakes occured in the meeting. For any two participants who have shaken hands, at most 1010 among the rest 2222 participants have shaken hands with exactly one of these two persons. Define a friend circle to be a group of 33 participants in which each person has shaken hands with the other two. Find the minimum possible value of friend circles.