(mathematics) A result in combinatorics, stating that every set of integers with positive natural density contains a k-term arithmetic progression for every k.

(geometry) A statement in Euclidean geometry that deals with the construction of a particular parallelogram (the Varignon parallelogram) from an arbitrary quadrilateral.

plural of no-go theorem

(logic) A theorem stating that, in any formal system F with Peano arithmetic, for any formula P, if it is provable in F that "if P is provable in F then P is true", then P is provable in F.

(graph theory) A theorem stating that, among the n-vertex simple graphs with no (r + 1)-cliques, T(n, r) has the maximum number of edges.

(physics) A theorem stating that the energy eigenstates for an electron in a crystal can be written as Bloch waves.

(graph theory) A characterization of the connectivity in finite undirected graphs in terms of the minimum number of disjoint paths that can be found between any pair of vertices.

plural of fundamental theorem

(chiefly mathematics) A theorem (or, in non-mathematical fields, a commonly accepted hypothesis) considered to be of central importance to a specified field.

The theorem that any graph labelling (with colours) of a sufficiently large complete graph contains monochromatic cliques.