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  2. Gallai–Edmonds decomposition - Wikipedia

    en.wikipedia.org/wiki/Gallai–Edmonds_decomposition

    In graph theory, the Gallai–Edmonds decomposition is a partition of the vertices of a graph into three subsets which provides information on the structure of maximum matchings in the graph. Tibor Gallai [1] [2] and Jack Edmonds [3] independently discovered it and proved its key properties. The Gallai–Edmonds decomposition of a graph can be ...

  3. Decomposition theorem of Beilinson, Bernstein and Deligne

    en.wikipedia.org/wiki/Decomposition_theorem_of...

    In mathematics, especially algebraic geometry, the decomposition theorem of Beilinson, Bernstein and Deligne or BBD decomposition theorem is a set of results concerning the cohomology of algebraic varieties. It was originally conjectured by Gelfand and MacPherson.

  4. Robertson–Seymour theorem - Wikipedia

    en.wikipedia.org/wiki/Robertson–Seymour_theorem

    Wagner's theorem states that a graph is planar if and only if it has neither K 5 nor K 3,3 as a minor. In other words, the set {K 5, K 3,3} is an obstruction set for the set of all planar graphs, and in fact the unique minimal obstruction set. A similar theorem states that K 4 and K 2,3 are the forbidden minors for the set of outerplanar graphs.

  5. Graph theory - Wikipedia

    en.wikipedia.org/wiki/Graph_theory

    The first textbook on graph theory was written by Dénes Kőnig, and published in 1936. [26] Another book by Frank Harary , published in 1969, was "considered the world over to be the definitive textbook on the subject", [ 27 ] and enabled mathematicians, chemists, electrical engineers and social scientists to talk to each other.

  6. Split (graph theory) - Wikipedia

    en.wikipedia.org/wiki/Split_(graph_theory)

    In graph theory, a split of an undirected graph is a cut whose cut-set forms a complete bipartite graph.A graph is prime if it has no splits. The splits of a graph can be collected into a tree-like structure called the split decomposition or join decomposition, which can be constructed in linear time.

  7. Modular decomposition - Wikipedia

    en.wikipedia.org/wiki/Modular_decomposition

    The decomposition depicted in the figure below is this special decomposition for the given graph. A graph, its quotient where "bags" of vertices of the graph correspond to the children of the root of the modular decomposition tree, and its full modular decomposition tree: series nodes are labeled "s", parallel nodes "//" and prime nodes "p".

  8. Perfect graph - Wikipedia

    en.wikipedia.org/wiki/Perfect_graph

    The perfect graph theorem has a short proof, [5] [6] but the proof of the strong perfect graph theorem is long and technical, based on a deep structural decomposition of Berge graphs. Related decomposition techniques have also borne fruit in the study of other graph classes, and in particular for the claw-free graphs . [ 16 ]

  9. Algebraic graph theory - Wikipedia

    en.wikipedia.org/wiki/Algebraic_graph_theory

    Algebraic graph theory is a branch of mathematics in which algebraic methods are applied to problems about graphs. This is in contrast to geometric, combinatoric, or algorithmic approaches. There are three main branches of algebraic graph theory, involving the use of linear algebra, the use of group theory, and the study of graph invariants.