n persons a a party, everyone dislikes only 1
Source: 2023 Czech-Polish-Slovak Match Junior, Team p3 CPSJ
May 5, 2024
combinatorics
Problem Statement
people met at the party, with . Each person dislikes exactly one other person present at the party (but not necessarily reciprocal, i.e. it may happen that dislikes even though does not dislike ) and likes all others. Prove that guests can be seated at three tables in such a way that each guest likes all the people at his table.