Upward Drawing on the Plane Grid Using Less Ink (Extended Abstract)Jourdan, GuyVincent and Rival, Ivan and Zaguia, Nejib (1995) Upward Drawing on the Plane Grid Using Less Ink (Extended Abstract). In: Graph Drawing DIMACS International Workshop, GD 1994, October 10–12, 1994 , pp. 318327(Official URL: http://dx.doi.org/10.1007/3540589503_387). Full text not available from this repository.
Official URL: http://dx.doi.org/10.1007/3540589503_387
AbstractAny upward drawing D(P) on a twodimensional integer grid I, of an ordered set P, has completion \bar{P} with an upward drawing D(\bar{P}) on a twodimensional integer grid \bar{I} such that the total edge length of D(\bar{P}) does not exceed the total edge length of D(P). Moreover, by (possibly) translating vertices, there is an upward drawing D(P) on I such that \bar{I} = I. Thus, any integer grid embedding of a twodimensional ordered set can be extended to a planar upward drawing of its completion, on the same integer grid, without increasing the total edge length.
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