Get Graph Drawing: 17th International Symposium, GD 2009, PDF

By János Pach (auth.), David Eppstein, Emden R. Gansner (eds.)

ISBN-10: 3642118046

ISBN-13: 9783642118043

ISBN-10: 3642118054

ISBN-13: 9783642118050

This quantity constitutes the refereed court cases 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 offered have been conscientiously reviewed and chosen out of seventy nine submissions. moreover, 10 posters have been approved in a separate submission method

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Extra info for Graph Drawing: 17th International Symposium, GD 2009, Chicago, IL, USA, September 22-25, 2009. Revised Papers

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C Springer-Verlag Berlin Heidelberg 2010 22 P. Angelini et al. new class of drawings, called Right Angle Crossing drawings (RAC drawings) [7]. A RAC drawing of a graph G is a polyline drawing D of G such that any two crossing segments in D are orthogonal. If D has curve complexity 0, D is a straight-line RAC drawing, where the curve complexity of D is the maximum number of bends along an edge of D. This paper continues the study of RAC drawings initiated in [7] and investigates RAC drawings with low curve complexity for both directed and undirected graphs.

2(a), that serves as a gadget for proving the main results of this section. The following lemmata show that two copies of H cannot cross each other in any RAC drawing. Let E1 , E2 , and E3 be the embeddings of H shown in Fig. 2(a), 2(b), and 2(c), respectively. Lemma 1. In any RAC drawing of H, its embedding is one of E1 , E2 , or E3 , up to a reversal of the adjacency lists of all the vertices. Let G be a digraph containing two copies H and H of H, with vertex sets {u , v , w , z } and {u , v , w , z }, respectively, so that one vertex in {u , v } possibly coincides with one in {u , v }, while no other vertex is shared by the two graphs.

We first describe how to draw the edges of cycle cover C2 above the diagonal. Consider an edge (u, v) of C2 and let u and v be placed at grid points (ux , uy ) and (vx , vy ), respectively. , uy < vy ), then edge (u, v) is drawn as a 3-segment line exiting vertex u from the Y -port and being defined by bend-points (ux , vy − 38 + 2 ) and (vx − 38 + 1 , vy − 38 + 2 ), 0 < 1 < 2 < 14 . Note that the second bend-point is located within the lightly-shaded region (above the diagonal) of the south-west quadrant of the square centered at vertex v (see Fig.

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Graph Drawing: 17th International Symposium, GD 2009, Chicago, IL, USA, September 22-25, 2009. Revised Papers by János Pach (auth.), David Eppstein, Emden R. Gansner (eds.)

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