Question 11
Consider a complete graph with 4046 vertices whose edges are colored in some colors. We call the graph $k$-good if all the vertices of the graph can be divided into 2023 pairs in such a way that among the colors of the 2023 edges connecting the vertices in the pairs there are exactly $k$ distinct colors. Is it possible that the graph is 999-good and 1001-good, but not 1000-good?
(Anton Trygub)
(Anton Trygub)