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Extremal Graph Theory
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 property, 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Turan 13-4
Turan (; ; , , ) is a historical region in Central Asia. The term is of Iranian origin and may refer to a particular prehistoric human settlement, a historic geographical region, or a culture. The original Turanians were an Iranian tribe of the Avestan age. Overview In ancient Iranian mythology, Tūr or Turaj (''Tuzh'' in Middle Persian) is the son of the emperor Fereydun. According to the account in the ''Shahnameh'', the nomadic tribes who inhabited these lands were ruled by Tūr. In that sense, the Turanians could be members of two Iranian peoples both descending from Fereydun, but with different geographical domains and often at war with each other. Turan, therefore, comprised five areas: the Kopet Dag region, the Atrek valley, parts of Bactria, Sogdia and Margiana. A later association of the original Turanians with Turkic peoples is based primarily on the subsequent Turkification of Central Asia, including the above areas. According to C. E. Bosworth, however ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Clique Number
In graph theory, a clique ( or ) is a subset of vertices of an undirected graph such that every two distinct vertices in the clique are adjacent. That is, a clique of a graph G is an induced subgraph of G that is complete. Cliques are one of the basic concepts of graph theory and are used in many other mathematical problems and constructions on graphs. Cliques have also been studied in computer science: the task of finding whether there is a clique of a given size in a graph (the clique problem) is NP-complete, but despite this hardness result, many algorithms for finding cliques have been studied. Although the study of complete subgraphs goes back at least to the graph-theoretic reformulation of Ramsey theory by , the term ''clique'' comes from , who used complete subgraphs in social networks to model cliques of people; that is, groups of people all of whom know each other. Cliques have many other applications in the sciences and particularly in bioinformatics. Definitions ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
