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  2. Petersen's theorem - Wikipedia

    en.wikipedia.org/wiki/Petersen's_theorem

    In the mathematical discipline of graph 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 cubic, bridgeless graph contains a perfect matching. [1] In other words, if a graph has exactly three edges at each vertex, and every edge belongs ...

  3. 2-factor theorem - Wikipedia

    en.wikipedia.org/wiki/2-factor_theorem

    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} .

  4. Julius Petersen - Wikipedia

    en.wikipedia.org/wiki/Julius_Petersen

    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’.

  5. Petersen graph - Wikipedia

    en.wikipedia.org/wiki/Petersen_graph

    Petersen graph as Kneser graph ,. The Petersen graph is the complement of the line graph of .It is also the Kneser graph,; this means that it has one vertex for each 2-element subset of a 5-element set, and two vertices are connected by an edge if and only if the corresponding 2-element subsets are disjoint from each other.

  6. Petersen family - Wikipedia

    en.wikipedia.org/wiki/Petersen_family

    The Petersen family. K 6 is at the top of the illustration, K 3,3,1 is in the upper right, and the Petersen graph is at the bottom. The blue links indicate ΔY- or YΔ-transforms between graphs in the family. In graph theory, the Petersen family is a set of seven undirected graphs that includes the Petersen graph and the complete graph K 6.

  7. Category:Theorems in graph theory - Wikipedia

    en.wikipedia.org/wiki/Category:Theorems_in_graph...

    Download as PDF; Printable version; In other projects Wikidata item; Appearance. move to sidebar hide. ... Perfect graph theorem; Petersen's theorem; Planar separator ...

  8. NYT ‘Connections’ Hints and Answers Today, Tuesday, December 10

    www.aol.com/nyt-connections-hints-answers-today...

    2. Phases of an aerial journey. 3. To search for something. 4. These words can be found on a map (if you add a letter to the beginning). Related: 300 Trivia Questions and Answers to Jumpstart Your ...

  9. Cubic graph - Wikipedia

    en.wikipedia.org/wiki/Cubic_graph

    According to Brooks' theorem every connected cubic graph other than the complete graph K 4 has a vertex coloring with at most three colors. Therefore, every connected cubic graph other than K 4 has an independent set of at least n/3 vertices, where n is the number of vertices in the graph: for instance, the largest color class in a 3-coloring has at least this many vertices.