(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.

(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.

(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).

(mathematics) A theorem about discrete dynamical systems. One of its implications is that if a discrete dynamical system on the real line has a periodic point of period 3, then it must have periodic points of every other period.

A mathematical theorem, important for quantum logic, proving that the Born rule for the probability of obtaining specific results for a given measurement follows naturally from the structure formed by the lattice of events in a real or complex Hilbert space.

(number theory) A theorem that gives a finite bound on the number of consecutive pairs of smooth numbers that exist, for a given degree of smoothness, and provides a method for finding all such pairs using Pell equations.

An important limitative theorem in quantum computing that establishes an upper bound (Holevo's bound) for the amount of information that can be known about a quantum state.

(mathematics) A result concerning certain infinite-dimensional vector spaces, stating that any orthomodular form that has an infinite orthonormal sequence is a Hilbert space over the real numbers, complex numbers or quaternions.

(mathematics) A basic result of algebraic topology, connecting homotopy theory with homology theory via a map known as the Hurewicz homomorphism.