MathDB
Simple Graph is not Simple

Source: 2019 Taiwan TST Round 3

April 2, 2020
combinatorics

Problem Statement

Given a simple graph with 4038 4038 vertices. Assume we arbitrarily choose 2019 2019 vertices as a group (the other 2019 2019 is another group, of course), there are always k k edges that connect two groups. Find all possible value of k k .