Editing Linkless embedding (section)

=== Graphs with small Colin de Verdière invariant ===

The [[Colin de Verdière graph invariant]] is an integer defined for any graph using [[algebraic graph theory]]. The graphs with Colin de Verdière graph invariant at most μ, for any fixed constant μ, form a minor-closed family, and the first few of these are well-known: the graphs with μ ≤ 1 are the linear forests (disjoint unions of paths), the graphs with μ ≤ 2 are the [[outerplanar graph]]s, and the graphs with μ ≤ 3 are the [[planar graph]]s. As {{harvtxt|Robertson|Seymour|Thomas|1993a}} conjectured and {{harvtxt|Lovász|Schrijver|1998}} proved, the graphs with μ ≤ 4 are exactly the linklessly embeddable graphs.