Albertson conjecture

Statement

In combinatorial mathematics, the Albertson conjecture is an unproven relationship between the crossing number and the chromatic number of a graph. It is named after Michael O. Albertson, a professor at Smith College, who stated it as a conjecture in 2007; it is one of his many conjectures in graph coloring theory. The conjecture states that, among all graphs requiring $n$ colors, the complete graph $K_n$ is the one with the smallest crossing number. Equivalently, if a graph can be drawn with fewer crossings than $K_n$, then, according to the conjecture, it may be colored with fewer than $n$ colors.