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extremal basis - translation to russian
![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.")
математика
экстремальный базис
![This picture illustrates the [[standard basis]] in '''R'''<sup>2</sup>. The blue and orange vectors are the elements of the basis; the green vector can be given in terms of the basis vectors, and so is [[linearly dependent]] upon them.](https://commons.wikimedia.org/wiki/Special:FilePath/Basis graph (no label).svg?width=200 "This picture illustrates the [[standard basis]] in '''R'''<sup>2</sup>. The blue and orange vectors are the elements of the basis; the green vector can be given in terms of the basis vectors, and so is [[linearly dependent]] upon them.")
![[−1, 1]<sup>''n''</sup>}} as a function of dimension, ''n''. Boxplots show the second and third quartiles of this data for each ''n'', red bars correspond to the medians, and blue stars indicate means. Red curve shows theoretical bound given by Eq. (1) and green curve shows a refined estimate.<ref name = "GorbanTyukin2016"/>](https://commons.wikimedia.org/wiki/Special:FilePath/Random almost orthogonal sets.png?width=200 "[−1, 1]<sup>''n''</sup>}} as a function of dimension, ''n''. Boxplots show the second and third quartiles of this data for each ''n'', red bars correspond to the medians, and blue stars indicate means. Red curve shows theoretical bound given by Eq. (1) and green curve shows a refined estimate.<ref name = \"GorbanTyukin2016\"/>")
математика
векторный базис
математика
упорядоченный базис
Definition
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.
