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  2. 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} .

  3. Graph factorization - Wikipedia

    en.wikipedia.org/wiki/Graph_factorization

    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. A k-factor of a graph is a spanning k-regular subgraph, and a k-factorization partitions the edges of the graph into disjoint k-factors. A graph G is said to be k-factorable if it admits a k ...

  4. Graph theory - Wikipedia

    en.wikipedia.org/wiki/Graph_theory

    In mathematics and computer science, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects.

  5. Logic of graphs - Wikipedia

    en.wikipedia.org/wiki/Logic_of_graphs

    The graph shown here appears as a subgraph of an undirected graph if and only if models the sentence ,,,.. In the first-order logic of graphs, a graph property is expressed as a quantified logical sentence whose variables represent graph vertices , with predicates for equality and adjacency testing.

  6. Glossary of graph theory - Wikipedia

    en.wikipedia.org/wiki/Glossary_of_graph_theory

    Spectral graph theory is the branch of graph theory that uses spectra to analyze graphs. See also spectral expansion. split 1. A split graph is a graph whose vertices can be partitioned into a clique and an independent set. A related class of graphs, the double split graphs, are used in the proof of the strong perfect graph theorem.

  7. YΔ- and ΔY-transformation - Wikipedia

    en.wikipedia.org/wiki/YΔ-_and_ΔY-transformation

    ΔY- and YΔ-transformations are a tool both in pure graph theory as well as applications. Both operations preserve a number of natural topological properties of graphs. . For example, applying a YΔ-transformation to a 3-vertex of a planar graph, or a ΔY-transformation to a triangular face of a planar graph, results again in a planar graph.

  8. The fruits and vegetables from Mexico that could see higher ...

    www.aol.com/fruits-vegetables-mexico-could-see...

    Yet economists say that in most instances, the importing companies — which in theory would be based in the U.S. — would bear those costs, and in many cases ultimately pass them along to their ...

  9. Petersen family - Wikipedia

    en.wikipedia.org/wiki/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.