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- Extremal_graph_theory abstract "Extremal graph theory is a branch of the mathematical field of graph theory. Extremal graph theory studies extremal (maximal or minimal) graphs which satisfy a certain property. Extremality can be taken with respect to different graph invariants, such as order, size or girth. More abstractly, it studies how global properties of a graph influence local substructures of the graph.For example, a simple extremal graph theory question is "which acyclic graphs on n vertices have the maximum number of edges?" The extremal graphs for this question are trees on n vertices, which have n − 1 edges. More generally, a typical question is the following. Given a graph property P, an invariant u, and a set of graphs H, we wish to find the minimum value of m such that every graph in H which has u larger than m possess property P. In the example above, H was the set of n-vertex graphs, P was the property of being cyclic, and u was the number of edges in the graph. Thus every graph on n vertices with more than n − 1 edges must contain a cycle.Several foundational results in extremal graph theory are questions of the above-mentioned form. For instance, the question of how many edges can an n-vertex graph have before it must contain as subgraph a clique of size k is answered by Turán's theorem. Instead of cliques, if the same question is asked for complete multi-partite graphs, the answer is given by the Erdős–Stone theorem.".
- Extremal_graph_theory wikiPageExternalLink index.html.
- Extremal_graph_theory wikiPageExternalLink BerlinG.pdf.
- Extremal_graph_theory wikiPageID "529568".
- Extremal_graph_theory wikiPageRevisionID "582202816".
- Extremal_graph_theory hasPhotoCollection Extremal_graph_theory.
- Extremal_graph_theory quote "Extremal graph theory, in its strictest sense, is a branch of graph theory developed and loved by Hungarians.".
- Extremal_graph_theory width "300".
- Extremal_graph_theory subject Category:Extremal_graph_theory.
- Extremal_graph_theory comment "Extremal graph theory is a branch of the mathematical field of graph theory. Extremal graph theory studies extremal (maximal or minimal) graphs which satisfy a certain property. Extremality can be taken with respect to different graph invariants, such as order, size or girth.".
- Extremal_graph_theory label "Extremal graph theory".
- Extremal_graph_theory label "Extremale Graphentheorie".
- Extremal_graph_theory label "Teoría de grafos extremales".
- Extremal_graph_theory label "Théorie des graphes extrémaux".
- Extremal_graph_theory sameAs Extremale_Graphentheorie.
- Extremal_graph_theory sameAs Teoría_de_grafos_extremales.
- Extremal_graph_theory sameAs Théorie_des_graphes_extrémaux.
- Extremal_graph_theory sameAs m.02m075.
- Extremal_graph_theory sameAs Q739245.
- Extremal_graph_theory sameAs Q739245.
- Extremal_graph_theory wasDerivedFrom Extremal_graph_theory?oldid=582202816.
- Extremal_graph_theory isPrimaryTopicOf Extremal_graph_theory.