(mathematics) An important structural theorem in the theory of Banach spaces, essentially stating that every sufficiently high-dimensional normed vector space will have low-dimensional subspaces that are approximately Euclidean.

(graph theory) A theorem that considers the sum of the degrees of pairs of non-adjacent vertices: if every such pair has a sum that at least equals the total number of vertices in the graph, then the graph is Hamiltonian.

(graph theory) The theorem stating that every cubic bridgeless graph contains a perfect matching.

(graph theory) A theorem stating that the set of edges of a finite graph can be written as a union of disjoint simple cycles if and only if every vertex has even degree.

(statistics) A theorem relating to the distribution of the likelihood ratio.

A theorem dealing with the relative probability that the entropy of a system that is currently away from thermodynamic equilibrium (i.e. maximum entropy) will increase or decrease over a given amount of time.

A theorem stating that two connected graphs are isomorphic if and only if their line graphs are isomorphic, with a single exception: K₃, the complete graph on three vertices, and the complete bipartite graph K_(1,3), which are not isomorphic but both have K₃ as their line graph.

(geometry) A theorem asserting that every valuation on convex bodies in Rⁿ that is continuous and invariant under rigid motions of Rⁿ is a linear combination of the quermassintegrals (or, equivalently, of the intrinsic volumes).

A parody of the three laws of thermodynamics in terms of a person playing a game: (1) you can't win; (2) you can't break even; (3) you can't even get out of the game.

(physics) A no-go theorem stating that no physical theory of local hidden variables can ever reproduce all of the predictions of quantum mechanics.