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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...

Chapter 8; Petersen 2016, Theorem 12.4.1; Sakai 1996, Theorem V.3.4. Petersen 2016, p. 462; Sakai 1996, Corollary V.3.5. Chow et al. 2010, Theorem I.25. Yau...

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...

counterexample to Tait's claimed theorem about 1-factorability of 3-regular graphs, which is nowadays known as the "Petersen graph". In cryptography and mathematical...

Besse 1987, Definition 6.64; Petersen 2016, p. 298; Schoen & Yau 1994, p. 12. Besse 1987, Section 6E; Petersen 2016, Theorem 7.3.5; Schoen & Yau 1994, Section...

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 the mathematical field of graph theory, the Petersen graph is an undirected graph with 10 vertices and 15 edges. It is a small graph that serves as...

the mathematical discipline of graph theory, the 2-factor theorem, discovered by Julius Petersen, is one of the earliest works in graph theory. It can be...

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

2.2; Milnor 1963, Lemma 8.6; O'Neill 1983, Theorem 3.11; Petersen 2016, Theorem 2.2.2; Wald 1984, Theorem 3.1.1. Jost 2017, Definition 4.2.1. do Carmo...

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

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...

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...

Preissmann 1943. do Carmo 1992, Theorem 12.3.2; Petersen 2016, Theorem 6.2.6. do Carmo 1992, Theorem 12.3.8. Jost 2017, Section 9.7. Bridson & Haefliger...

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...

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...

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

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...

Section IV.4; Lang 1999, Section VIII.6; O'Neill 1983, Theorem 5.21 and Proposition 5.22; Petersen 2016, Section 5.7.1. Bridson & Haefliger 1999, Proposition...