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Was (wer) ist extremal distribution - definition
![The [[Petersen graph]] has chromatic number 3.](https://commons.wikimedia.org/wiki/Special:FilePath/Petersen graph 3-coloring.svg?width=200 "The [[Petersen graph]] has chromatic number 3.")
![[[Harrods]]' food hall, a major retailer in London](https://commons.wikimedia.org/wiki/Special:FilePath/London, Harrods (2).JPG?width=200 "[[Harrods]]' food hall, a major retailer in London")
![A wholesale fish market at [[Haikou New Port]], China](https://commons.wikimedia.org/wiki/Special:FilePath/Wholesale fish market at Haikou New Port - 14.jpg?width=200 "A wholesale fish market at [[Haikou New Port]], China")
![arc-lamp]] lighting used outdoors or in large indoor spaces, such as this [[Brush Electric Company]] system installed in 1880 in [[New York City]].](https://commons.wikimedia.org/wiki/Special:FilePath/Brush Company arc light madison square new york 1882.png?width=200 "arc-lamp]] lighting used outdoors or in large indoor spaces, such as this [[Brush Electric Company]] system installed in 1880 in [[New York City]].")
![electricity networks]]. The voltages and loadings are typical of a European network.](https://commons.wikimedia.org/wiki/Special:FilePath/Electricity Grid Schematic English.svg?width=200 "electricity networks]]. The voltages and loadings are typical of a European network.")
![Substation near [[Yellowknife]], in the Northwest Territories of Canada](https://commons.wikimedia.org/wiki/Special:FilePath/NCPC Power Plant Yellowknife Northwest Territories Canada 08.jpg?width=200 "Substation near [[Yellowknife]], in the Northwest Territories of Canada")
![High voltage power pole in rural [[Butte County, California]]](https://commons.wikimedia.org/wiki/Special:FilePath/Red-tailed hawk on power pole-2033.jpg?width=200 "High voltage power pole in rural [[Butte County, California]]")
Wikipedia
Extremal graph theory is a branch of combinatorics, itself an area of mathematics, that lies at the intersection of extremal combinatorics and graph theory. In essence, extremal graph theory studies how global properties of a graph influence local substructure. Results in extremal graph theory deal with quantitative connections between various graph properties, both global (such as the number of vertices and edges) and local (such as the existence of specific subgraphs), and problems in extremal graph theory can often be formulated as optimization problems: how big or small a parameter of a graph can be, given some constraints that the graph has to satisfy? A graph that is an optimal solution to such an optimization problem is called an extremal graph, and extremal graphs are important objects of study in extremal graph theory.
Extremal graph theory is closely related to fields such as Ramsey theory, spectral graph theory, computational complexity theory, and additive combinatorics, and frequently employs the probabilistic method.
