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An orthogonal ray graph is an intersection graph of horizontal and vertical rays (half-lines) in the xy-plane. An orthogonal ray graph is a 2-directional orthogonal ray graph if all the horizontal rays extend in the positive a;-direction and all the vertical rays extend in the positive x-direction. We show several characterizations of 2-directional orthogonal ray graphs. We first show a forbidden...
It has been known that every series-parallel 6-graph has a 2-bend 3D orthogonal drawing, while it has been open whether every series-parallel 6-graph has a 1-bend 3D orthogonal drawing. We show in this paper that every outerplanar 5-graph has a 1-bend 3D orthogonal drawing.
The logic mapping problem and the problem of finding a largest square sub-crossbar with no defects in a nano-crossbar with nonprogrammable crosspoint defects and disconnected wire defects have been known to be NP-hard. This paper shows that for nano-crossbars with only disconnected wire defects, the former remains NP-hard, while the latter can be solved in polynomial time.
It has been known that every 6-graph has a 3-bend 3-D orthogonal drawing, while it has been open whether every 6- graph has a 2-bend 3-D orthogonal drawing. For the interesting open question, it is known that every 5-graph has a 2-bend 3-D orthogonal drawing, and every outerplanar 6-graph without triangles has a O-bend 3-D orthogonal drawing. We show in this paper that every series-parallel 6-graph...
It has been known that every planar 4-graph has a 2-bend 2D orthogonal drawing with the only exception of octahedron, every planar 3-graph has a 1-bend 2D orthogonal drawing with the only exception of K 4, and every outerplanar 3-graph with no triangles has a 0-bend 2D orthogonal drawing. We show in this paper that every series-parallel 4-graph has a 1-bend 2D orthogonal drawing
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