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 Kn is the one with the smallest crossing number.Equivalently, if a graph can be drawn with fewer crossings than Kn, then, according to the conjecture, it may be colored with fewer than n colors.