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In 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 stated as follows: [ 1 ] Let G {\displaystyle G} be a regular graph whose degree is an even number, 2 k {\displaystyle 2k} .
1-factorization of the Desargues graph: each color class is a 1-factor. The Petersen graph can be partitioned into a 1-factor (red) and a 2-factor (blue). However, the graph is not 1-factorable. In graph theory, a factor of a graph G is a spanning subgraph, i.e., a subgraph that has the same vertex set as G.
By orienting the 2-factor, the edges of the perfect matching can be extended to paths of length three, say by taking the outward-oriented edges. This shows that every cubic, bridgeless graph decomposes into edge-disjoint paths of length three. [2] Petersen's theorem can also be applied to show that every maximal planar graph can be decomposed ...
In graph theory, two of Petersen's most famous contributions are: the Petersen graph, exhibited in 1898, served as a counterexample to Tait's ‘theorem’ on the 4-colour problem: a bridgeless 3-regular graph is factorable into three 1-factors and the theorem: ‘a connected 3-regular graph with at most two leaves contains a 1-factor’.
2-factor theorem; A. Alspach's conjecture; B. Balinski's theorem; ... Graph structure theorem; Grinberg's theorem; Grötzsch's theorem; H. Hall-type theorems for ...
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A Catholic nun with the Sisters of Charity Institute in Milan was among 25 people arrested early Thursday morning for a litany of mafia-related crimes, including aiding and abetting extortion ...
2-factor theorem (graph theory) 15 and 290 theorems (number theory) 2π theorem (Riemannian geometry) A. AF+BG theorem (algebraic geometry) ATS theorem (number theory)