Colorability in Orthogonal Graph Drawing
Stola, Jan (2008) Colorability in Orthogonal Graph Drawing. In: Graph Drawing 15th International Symposium, GD 2007, September 24-26, 2007, Sydney, Australia , pp. 327-338 (Official URL: http://dx.doi.org/10.1007/978-3-540-77537-9_32).
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This paper studies the question: What is the maximum integer k_b,n such that every k_b,n-colorable graph has a b-bend n-dimensional orthogonal box drawing? We give an exact answer for the orthogonal line drawing in all dimensions and for the 3-dimensional rectangle visibility representation. We present an upper and lower bound for the 3-dimensional orthogonal drawing by rectangles and general boxes. Particularly, we improve the best known upper bound for the 3-dimensional orthogonal box drawing from 183 to 42 and the lower bound from 3 to 22.
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