کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
417932 | 681592 | 2016 | 12 صفحه PDF | دانلود رایگان |
An orthogonal ray graph is an intersection graph of horizontal rays (closed half-lines) and vertical rays in the plane, which is introduced in connection with the defect-tolerant design of nano-circuits. An orthogonal ray graph is a 3-directional orthogonal ray graph if every vertical ray has the same direction. A 3-directional orthogonal ray graph is a 2-directional orthogonal ray graph if every horizontal ray has the same direction. The characterizations and the complexity of the recognition problem have been open for orthogonal ray graphs and 3-directional orthogonal ray graphs, while various characterizations with a quadratic-time recognition algorithm have been known for 2-directional orthogonal ray graphs. In this paper, we show several characterizations with a linear-time recognition algorithm for orthogonal ray trees by using the 2-directional orthogonal ray trees. We also show that a tree is a 3-directional orthogonal ray graph if and only if it is a 2-directional orthogonal ray graph. Moreover, we show some necessary conditions for orthogonal ray graphs and 3-directional orthogonal ray graphs.
Journal: Discrete Applied Mathematics - Volume 201, 11 March 2016, Pages 201–212