A characterization of complete bipartite RAC graphs

Didimo, Walter; Eades, Peter; Liotta, Giuseppe

doi:10.1016/j.ipl.2010.05.023

Cited by 31 publications

(19 citation statements)

References 6 publications

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“…Di Giacomo et al [6] studied the interplay between the crossing resolution, the maximum number of bends per edges and the required area. Didimo et al [8] presented a characterization of complete bipartite graphs that admit a straightline RAC drawing. Arikushi et al [3] studied polyline RAC drawings in which each edge has at most one or two bends and proved that the number of edges is at most O(n) and O(n log 2 n), respectively.…”

Section: Related Workmentioning

confidence: 99%

“…However, recent eyetracking experiments by Huang et al [15,16] indicate that the negative impact of an edge crossing is eliminated in the case where the crossing angle is greater than 70 degrees. These results motivated the study of a new class of drawings, called rightangle drawings or RAC drawings for short [1,6,7,8]. A RAC drawing of a graph is a polyline drawing in which every pair of crossing edges intersects at right angle.…”

Section: Introductionmentioning

confidence: 99%

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The Straight-Line RAC Drawing Problem Is NP-Hard

Argyriou

Bekos

Symvonis

2011

SOFSEM 2011: Theory and Practice of Computer Science

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Abstract. Recent cognitive experiments have shown that the negative impact of an edge crossing on the human understanding of a graph drawing, tends to be eliminated in the case where the crossing angles are greater than 70 degrees. This motivated the study of RAC drawings, in which every pair of crossing edges intersects at right angle. In this work, we demonstrate a class of graphs with unique RAC combinatorial embedding and we employ members of this class in order to show that it is N P-hard to decide whether a graph admits a straight-line RAC drawing.

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Section: Related Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The Straight-Line RAC Drawing Problem Is NP-Hard

Argyriou

Bekos

Symvonis

2011

SOFSEM 2011: Theory and Practice of Computer Science

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“…Note that numerous papers on RAC-and large angle crossing graphs have recently appeared [2,7,13,11,25]. …”

Section: Previous Workmentioning

confidence: 99%

Untitled

Dujmović¹,

Gudmundsson²,

Morin³

et al. 2011

Chicago J. of Theoretical Comp. Sci.

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A geometric graph G is an α angle crossing (αAC) graph if every pair of crossing edges in G cross at an angle of at least α. The concept of right angle crossing (RAC) graphs (α = π/2) was recently introduced by Didimo et al. [10]. It was shown that any RAC graph with n vertices has at most 4n − 10 edges and that there are infinitely many values of n for which there exists a RAC graph with n vertices and 4n − 10 edges. In this paper, we give upper and lower bounds for the number of edges in αAC graphs for all 0 < α < π/2.

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“…Two main kinds of drawings have been considered: Drawings with crossing angle resolution π 2 (the largest possible value), called Right Angle Crossing drawings (or RAC drawings) (see, e.g., [2,4,5,8,10,11,13,18]), and drawings whose crossing angle resolution is at least a given α ∈ (0, π 2 ) (see, e.g., [1,7,9,12]). …”

Section: Introductionmentioning

confidence: 99%