Schnyder's theorem, in graph theory, characterizes planar graphs in terms of the order dimension of their incidence posets, the partial orders formed by a graph's vertices and edges ordered by which vertices are endpoints of which edges. Walter Schnyder proved in 1989 that a graph is planar if and only if the order dimension of its incidence poset, the smallest number of linear orderings whose intersection produces that partial order, does not exceed three. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/
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Source Schnyder's theorem (Wikipedia)
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1. Wikipedia: Schnyder's theorem
WikipediaLead section, statement-form referenceQuote, Lead section, statement-form reference
Schnyder's theorem states that a graph G is planar if and only if the order dimension of P(G) is at most three.
2. Schnyder's theorem (Wikipedia)
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In graph theory, Schnyder's theorem is a characterization of planar graphs in terms of the order dimension of their incidence posets.
In Branch: Graph Theory, Lead sentence
In graph theory, Schnyder's theorem is a characterization of planar graphs in terms of the order dimension of their incidence pose
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