By János Pach (auth.), David Eppstein, Emden R. Gansner (eds.)
This quantity constitutes the refereed complaints of the seventeenth foreign Symposium on Graph Drawing, GD 2009, held in Chicago, united states, in the course of September 2009. The 31 revised complete papers and four brief papers provided have been rigorously reviewed and chosen out of seventy nine submissions. moreover, 10 posters have been permitted in a separate submission technique
Read Online or Download Graph Drawing: 17th International Symposium, GD 2009, Chicago, IL, USA, September 22-25, 2009. Revised Papers PDF
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Additional resources for Graph Drawing: 17th International Symposium, GD 2009, Chicago, IL, USA, September 22-25, 2009. Revised Papers
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Springer, Heidelberg (2001) 13. : Upward planarity testing of outerplanar dags. G. ) GD 1994. LNCS, vol. 894, pp. 298–306. Springer, Heidelberg (1995) 14. : Algorithms for area-efficient orthogonal drawings. Computational Geometry 9(1-2), 83–110 (1998) 15. : Die theorie der regul¨aren graphen. Acta Mathematicae 15, 193–220 (1891) 16. : Effective information visualisation: a study of graph drawing aesthetics and algorithms. Interacting with Computers 13(2), 147–162 (2000) 17. : Empirical evaluation of aesthetics-based graph layout.
6(b)). Theorem 8. There exist kite-triangulations that do not admit straight-line RAC drawings. Proof. Consider the graph H in Fig. 6(c). Triangle (u, a, z) and vertices v, x, y create the forbidden structure of Property 2. Hence, every kite-triangulation G containing H as a subgraph requires one bend in any RAC drawing. Planar graphs are a proper subset of straight-line RAC drawable graphs. , [3,18]), straight-line RAC drawings may require larger area, as shown in the following. Theorem 9. There exists an n-vertex kite-triangulation that requires Ω(n3 ) area in any straight-line grid RAC drawing.
B) A straight-line RAC drawing of G. Proof. Consider a triangulation G defined as follows (see Fig. 7(a)). Let C = (u1 , u2 , . . , un−4 , un−3 ) be a simple cycle, for some odd integer n. Insert a vertex un−2 inside C and connect it to ui , with i = 1, 2, . . , n − 3. Insert two vertices un−1 and un outside C. Connect un−1 to ui , with i = 1, 2, . . , n − 6 and to un−3 ; connect un to un−6 , un−5 , un−4 , un−3 , and un−1 . Let G be the kite-triangulation obtained from G by adding edges (ui , ui+2 ), for i = 1, 3, 5, .