---
tag: 3SWZNY66QZ
kind: conjecture
name: Albertson conjecture
sources:
  - wikipedia: en:24205238@r1335680995
    locator: Albertson conjecture
    note: adopted
    mention: wikipedia://en/24205238
    sections: [Statement]
same_as:
  wikidata: Q4712279
  wikipedia: Albertson conjecture
inventory: [YC0GN15X1J]
---

## Statement

In [[combinatorial|0JKW7W7XFR]] mathematics, the **Albertson conjecture** is an unproven relationship between the crossing number and the chromatic number of a [[graph|00C0BR7D7H]]. 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|0NCPXH194Y]] theory. The conjecture states that, among all graphs requiring $n$ colors, the [[complete graph|03WKB2H474]] $K_n$ 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.