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intersection graph : ウィキペディア英語版
intersection graph

In the mathematical area of graph theory, an intersection graph is a graph that represents the pattern of intersections of a family of sets. Any graph can be represented as an intersection graph, but some important special classes of graphs can be defined by the types of sets that are used to form an intersection representation of them.
For an overview of both the theory of intersection graphs and important special classes of intersection graphs, see .
==Formal definition==
Formally, an intersection graph is an undirected graph formed from a family of sets
:''S''''i'', ''i'' = 0, 1, 2, ...
by creating one vertex ''v''''i'' for each set ''S''''i'', and connecting two vertices ''v''''i'' and ''v''''j'' by an edge whenever the corresponding two sets have a nonempty intersection, that is,
:''E''(''G'') =  | ''S''''i'' ∩ ''S''''j'' ≠ ∅}.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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