Engineers in a conference
Source: China TSTST 2017 Test 2 Day 1 Q2
March 13, 2017
graph theorycombinatorics
Problem Statement
engineers attend a conference. Any two engineers if they converse, converse with each other in either Chinese or English. No two engineers converse with each other more than once. It is known that within any four engineers, there was an even number of conversations and furthermore within this even number of conversations:i) At least one conversation is in Chinese.
ii) Either no conversations are in English or the number of English conversations is at least that of Chinese conversations.Show that there exists engineers such that any two of them conversed with each other in Chinese.