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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 boxdoi:10.1007/978-3-540-77537-9_32 dblp:conf/gd/Stola07 fatcat:u3itwjooc5cp3k5zoabhddmd2y