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Whitney's planarity criterion
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Whitney's planarity criterion : ウィキペディア英語版
Whitney's planarity criterion

In mathematics, Whitney's planarity criterion is a matroid-theoretic characterization of planar graphs, named after Hassler Whitney.〔.〕 It states that a graph is planar if and only if its graphic matroid is also cographic (that is, it is the dual matroid of another graphic matroid).
==Algebraic duals==
An equivalent form of Whitney's criterion is that a graph ''G'' is planar if and only if it has a dual graph whose graphic matroid is dual to the graphic matroid of ''G''.
A graph whose graphic matroid is dual to the graphic matroid of ''G'' is known as an algebraic dual of ''G''. This, Whitney's planarity criterion can be expressed succinctly as: a graph is planar if and only if it has an algebraic dual.

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