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Drawing SeriesParallel Graphs on a Box
 The University of Lethbridge
, 1997
"... A box is a restricted portion of the threedimensional integer grid consisting of four parallel lines of in nite length placed one grid unit apart. A boxdrawing of a graph is a straightline crossingfree drawing where vertices are located at integer grid points along the four lines. It is known t ..."
Abstract

Cited by 17 (3 self)
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A box is a restricted portion of the threedimensional integer grid consisting of four parallel lines of in nite length placed one grid unit apart. A boxdrawing of a graph is a straightline crossingfree drawing where vertices are located at integer grid points along the four lines. It is known that some planar graphs with triconnected components do not admit a boxdrawing. This paper shows that even structurally simpler planar graphs, namely seriesparallel graphs, are not boxdrawable in general. On the positive side, it is proved that every seriesparallel graph whose vertices have maximum degree at most three is boxdrawable. A drawing algorithm is presented that computes a box drawing of a 3planar seriesparallel graph in optimal time and with optimal volume.