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Graph structure theorem information


In mathematics, the graph structure theorem is a major result in the area of graph theory. The result establishes a deep and fundamental connection between the theory of graph minors and topological embeddings. The theorem is stated in the seventeenth of a series of 23 papers by Neil Robertson and Paul Seymour. Its proof is very long and involved. Kawarabayashi & Mohar (2007) and Lovász (2006) are surveys accessible to nonspecialists, describing the theorem and its consequences.

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Graph structure theorem

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In mathematics, the graph structure theorem is a major result in the area of graph theory. The result establishes a deep and fundamental connection between...

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Hamiltonian path

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Ore's theorems basically state that a graph is Hamiltonian if it has enough edges. The Bondy–Chvátal theorem operates on the closure cl(G) of a graph G with...

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Graph minor

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conjectures involving graph minors include the graph structure theorem, according to which the graphs that do not have H as a minor may be formed by gluing...

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Line graph

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underlying graph from vertices into edges, and by Whitney's theorem the same translation can also be done in the other direction. Line graphs are claw-free...

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List of theorems

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2-factor theorem (graph theory) 15 and 290 theorems (number theory) 2π theorem (Riemannian geometry) AF+BG theorem (algebraic geometry) ATS theorem (number...

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Planar graph

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consequence, planar graphs also have treewidth and branch-width O(√n). The planar product structure theorem states that every planar graph is a subgraph of...

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Perfect graph

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graph theorem states that the complement graph of a perfect graph is also perfect. The strong perfect graph theorem characterizes the perfect graphs in...

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Bipartite graph

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strong perfect graph theorem, the perfect graphs have a forbidden graph characterization resembling that of bipartite graphs: a graph is bipartite if...

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Graph isomorphism

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isomorphic but both have K3 as their line graph. The Whitney graph theorem can be extended to hypergraphs. While graph isomorphism may be studied in a classical...

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Graph coloring

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graph theory, graph coloring is a special case of graph labeling; it is an assignment of labels traditionally called "colors" to elements of a graph subject...

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Cayley graph

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Cayley graph, also known as a Cayley color graph, Cayley diagram, group diagram, or color group, is a graph that encodes the abstract structure of a group...

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Graph theory

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mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context...

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Structured program theorem

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The structured program theorem, also called the Böhm–Jacopini theorem, is a result in programming language theory. It states that a class of control-flow...

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List of graph theory topics

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graph Edge-transitive graph Interval graph Interval graph, improper Interval graph, proper Line graph Lollipop graph Minor Robertson–Seymour theorem Petersen...

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Topological graph theory

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circuit boards. Graph embeddings are also used to prove structural results about graphs, via graph minor theory and the graph structure theorem. Crossing number...

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Graph homomorphism

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the mathematical field of graph theory, a graph homomorphism is a mapping between two graphs that respects their structure. More concretely, it is a function...

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Glossary of graph theory

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Appendix:Glossary of graph theory in Wiktionary, the free dictionary. This is a glossary of graph theory. Graph theory is the study of graphs, systems of nodes...

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Planar separator theorem

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In graph theory, the planar separator theorem is a form of isoperimetric inequality for planar graphs, that states that any planar graph can be split...

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