File:Tractable points of the Tutte polynomial in the real plane.svg

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Summary

Description	English: The tractable points of the Tutte Polynomial in the real plane. Points in red are tractable over general graphs while the points in blue are #P-hard over general graphs but tractable over planar graphs. The red curve is the hyperbola $(x-1)(y-1)=1$ while the blue curve is the hyperbola $(x-1)(y-1)=2$ .
Date	11 November 2011
Source	Mathematica source code: minVal = -2.5; maxVal = 4.5; Show[ Plot[1/(x - 1) + 1, {x, minVal, maxVal}, Exclusions -> {1}, PlotStyle -> {Red, Thickness[Large]}, PlotRange -> {{minVal, maxVal}, {minVal, maxVal}}], Plot[2/(x - 1) + 1, {x, minVal, maxVal}, Exclusions -> {1}, PlotStyle -> {Blue, Thickness[Large]}, PlotRange -> {{minVal, maxVal}, {minVal, maxVal}}], ListPlot[{{1, 1}, {-1, -1}, {-1, 0}, {0, -1}}, PlotStyle -> {Red, PointSize[0.02]}], GridLines -> Automatic, GridLinesStyle -> Directive[Dashed], AxesLabel -> {x, y}, AspectRatio -> 1]
Author	Self

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	Date/Time	Thumbnail	Dimensions	User	Comment
current	03:11, 22 November 2011		360 × 361 (42 KB)	wikimediacommons>Bender2k14	(Probably) includes fix so that the blue hyperbola does not leave the plot range

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