Question 74
A convex $2019$-gon is given, for which no three diagonals intersect in a point. An intersection point of two diagonals, internal for the given polygon will be called “knot”. Two knots are called “neighbors” if they share a common diagonal. A closed path between neighboring knots, such that no three consecutive knots share a diagonal, will be called “cycle”. Find the maximal number of knots that can be colored, such that there exists no colored cycle (that is a cycle, containing only colored knots)?