21,484 research outputs found

    Transforming planar graph drawings while maintaining height

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    There are numerous styles of planar graph drawings, notably straight-line drawings, poly-line drawings, orthogonal graph drawings and visibility representations. In this note, we show that many of these drawings can be transformed from one style to another without changing the height of the drawing. We then give some applications of these transformations

    Straightening out planar poly-line drawings

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    We show that any yy-monotone poly-line drawing can be straightened out while maintaining yy-coordinates and height. The width may increase much, but we also show that on some graphs exponential width is required if we do not want to increase the height. Likewise yy-monotonicity is required: there are poly-line drawings (not yy-monotone) that cannot be straightened out while maintaining the height. We give some applications of our result.Comment: The main result turns out to be known (Pach & Toth, J. Graph Theory 2004, http://onlinelibrary.wiley.com/doi/10.1002/jgt.10168/pdf
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