Drawing 2-, 3- and 4-colorable Graphs in O(n²) Volume

Calamoneri, Tiziana and Sterbini, Andrea (1997) Drawing 2-, 3- and 4-colorable Graphs in O(n²) Volume. In: Symposium on Graph Drawing, GD '96, September 18-20, 1996, Berkeley, California, USA , pp. 53-62 (Official URL: http://dx.doi.org/10.1007/3-540-62495-3_37).

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Abstract

A Fary grid drawing of a graph is a drawing on a three-dimensional grid such that vertices are placed at integer coordinates and edges are straight-lines such that no edge crossings are allowed. In this paper it is proved that each k-colorable graph (k>=2) needs at leas1. t \Omega (n^(3/2)) volume to be drawn. Furthermore, it is shown how to draw 2-, 3- and 4-colorable graphs in a Fary grid fashion in O(n²) volume.

Item Type:Conference Paper
Additional Information:10.1007/3-540-62495-3_37
Classifications:G Algorithms and Complexity > G.999 Others
P Styles > P.060 3D
ID Code:64

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References

R. F. Cohen, P. Eades, T. Lin and F. Ruskey: Three-dimensional graph drawing, In Proc. GD '94, LNCS 894, pp. 1-11, 1994.

I. Fary: On straight lines representations of planar graphs, Acta Sci. Math. Szeged, 11, pp. 229-233, 1948.

G. Frank, D. Hui and C. Ware: Visualizing object oriented software in three dimensions, In Proc. CASCON, 1993.

J. MacKinley, G. Robertson and S. Card: Cone trees: Animated 3d visualization of hierarchical information, In Proc. SIGCHI Conf. on Human Factors in Computing, pp. 189-194, 1991.

P. Reid: Dynamic interactive display of complex data structures, In Graphics Tools for Software Engineers, pp. 62-70, Cambridge, 1989.

O. Tversky, S. Snibbe and R. Zeleznik: Cone trees in the uga graphics system: suggestions of a more robust visualization tool, Technical Report CS-93-07, Brown University, 1993.