theory, Petersen's theorem, named after Julius Petersen, is one of the earliest results in graph theory and can be stated as follows: Petersen's Theorem. Every...

the theorem that any bridgeless 3-regular graph can be decomposed into a l-factor and a 2-factor (Petersen's theorem). Between 1887 and 1895 Petersen also...

of graph theory. The theorem appears first in the 1891 article "Die Theorie der regulären graphs". To prove the theorem, Petersen's fundamental idea was...

Bipartite matching Hall's marriage theorem Petersen's theorem Lovász & Plummer (1986), p.  84; Bondy & Murty (1976), Theorem 5.4, p. 76. Bondy & Murty (1976)...

In geometry, the Petersen–Morley theorem states that, if a, b, c are three general skew lines in space, if a′, b′, c′ are the lines of shortest distance...

graph theory, that every cubic graph has an even number of vertices. Petersen's theorem states that every cubic bridgeless graph has a perfect matching. Lovász...

color. It has a list coloring with 3 colors, by Brooks' theorem for list colorings. The Petersen graph has chromatic index 4; coloring the edges requires...

This result, also known as the Petersen–Middleton theorem, is a generalization of the Nyquist–Shannon sampling theorem for sampling one-dimensional band-limited...

10-vertex 15-edge graph frequently used as a counterexample. 3.  Petersen's theorem that every bridgeless cubic graph has a perfect matching. planar A...

In mathematics, the soul theorem is a theorem of Riemannian geometry that largely reduces the study of complete manifolds of non-negative sectional curvature...

In mathematics, the four color theorem, or the four color map theorem, states that no more than four colors are required to color the regions of any map...

of Petersen's theorem", Annals of Mathematics, Second Series, 27 (4): 491–493, doi:10.2307/1967699, ISSN 0003-486X, JSTOR 1967699 Petersen's theorem "Orrin...

theorem holds are conservative systems; thus all ergodic systems are conservative. More precise information is provided by various ergodic theorems which...

splitting theorems on when a pseudo-Riemannian manifold can be given as a metric product. The best-known is the Cheeger–Gromoll splitting theorem for Riemannian...

making with László Lovász the now-proven conjecture (generalizing Petersen's theorem) that every bridgeless cubic graph has an exponential number of perfect...

graph has an exponential number of perfect matchings, strengthening Petersen's theorem that at least one perfect matching exists. In a pair of papers with...

Wetensch. Indag. Math., 82 (1): 83–86, doi:10.1016/1385-7258(79)90012-X Petersen's theorem Voorhoeve, Marc (1976), "On the oscillation of exponential polynomials"...

In mathematics, the convolution theorem states that under suitable conditions the Fourier transform of a convolution of two functions (or signals) is...

In graph theory, Kuratowski's theorem is a mathematical forbidden graph characterization of planar graphs, named after Kazimierz Kuratowski. It states...

the Bondy–Chvátal theorem, which generalizes earlier results by G. A. Dirac (1952) and Øystein Ore. Both Dirac's and Ore's theorems can also be derived...

conditions hold for v ≥ 3: Theorem 1. e ≤ 3v − 6; Theorem 2. If there are no cycles of length 3, then e ≤ 2v − 4. Theorem 3. f ≤ 2v − 4. In this sense...

curvature then the sum of its Betti numbers is at most C. Grove–Petersen's finiteness theorem. Given constants C, D and V, there are only finitely many homotopy...

The Hopf–Rinow theorem is a set of statements about the geodesic completeness of Riemannian manifolds. It is named after Heinz Hopf and his student Willi...

compactness theorem for sequences of metric spaces. In the special case of Riemannian manifolds, the key assumption of his compactness theorem is automatically...

that the four color theorem is equivalent to the statement that no snark is planar. The first graph known to be a snark was the Petersen graph; it was proved...

In graph theory, the Robertson–Seymour theorem (also called the graph minors theorem) states that the undirected graphs, partially ordered by the graph...

a comparison theorem in Riemannian geometry, named after Richard L. Bishop and Mikhail Gromov. It is closely related to Myers' theorem, and is the key...

Van der Waerden's theorem is a theorem in the branch of mathematics called Ramsey theory. Van der Waerden's theorem states that for any given positive...

The fundamental theorem of Riemannian geometry states that on any Riemannian manifold (or pseudo-Riemannian manifold) there is a unique affine connection...

Vizing's theorem. The generalized Petersen graph G(9, 2) is one of the few graphs known to have only one 3-edge-coloring. A 4-edge-coloring of the Petersen graph...