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- Tutte_embedding abstract "In graph drawing and geometric graph theory, a Tutte embedding or barycentric embedding of a 3-vertex-connected planar graph is a crossing-free straight-line embedding with the properties that the outer face is a convex polygon and that each interior vertex is at the average (or barycenter) of its neighbor's positions. If the outer polygon is fixed, this condition on the interior vertices determines their position uniquely as the solution to a system of linear equations. Solving the equations geometrically produces a Schlegel diagram. Tutte's spring theorem, proven by W. T. Tutte (1963), states that this unique solution is always crossing-free, and more strongly that every face of the resulting planar embedding is convex. It is called the spring theorem because such an embedding can be found as the equilibrium position for a system of springs representing the edges of the graph.".
- Tutte_embedding thumbnail Tutte_cube.svg?width=300.
- Tutte_embedding wikiPageID "39503349".
- Tutte_embedding wikiPageRevisionID "600431494".
- Tutte_embedding authorlink "W. T. Tutte".
- Tutte_embedding first "W. T.".
- Tutte_embedding last "Tutte".
- Tutte_embedding year "1963".
- Tutte_embedding subject Category:Graph_drawing.
- Tutte_embedding subject Category:Planar_graphs.
- Tutte_embedding comment "In graph drawing and geometric graph theory, a Tutte embedding or barycentric embedding of a 3-vertex-connected planar graph is a crossing-free straight-line embedding with the properties that the outer face is a convex polygon and that each interior vertex is at the average (or barycenter) of its neighbor's positions. If the outer polygon is fixed, this condition on the interior vertices determines their position uniquely as the solution to a system of linear equations.".
- Tutte_embedding label "Tutte embedding".
- Tutte_embedding sameAs m.0vpyrqx.
- Tutte_embedding sameAs Q17090559.
- Tutte_embedding sameAs Q17090559.
- Tutte_embedding wasDerivedFrom Tutte_embedding?oldid=600431494.
- Tutte_embedding depiction Tutte_cube.svg.
- Tutte_embedding isPrimaryTopicOf Tutte_embedding.