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The Same Upper Bound for Both: The 2‐page and the Rectilinear Crossing Numbers of the n‐Cube
Authors:Luerbio Faria  Celina M. H. de Figueiredo  R. Bruce Richter  Imrich Vrt'o
Affiliation:1. DEPARTMENT OF COMPUTATION, UNIVERSITY OF THE STATE OF RIO DE JANEIRO, RIO DE JANEIRO, BRAZIL;2. COPPE—SYSTEMS ENGINEERING AND COMPUTER SCIENCE, FEDERAL UNIVERSITY OF RIO DE JANEIRO, RIO DE JANEIRO, BRAZILContract grant sponsors: CNPq, CAPES, FAPERJ, FINEP, and NSERC;3. Contract grant sponsor: Slovak Research and Development Agency;4. Contract grant number: ESF‐EC‐0009‐10;5. Contract grant sponsor: VEGA;6. Contract grant number: 2/0136/12.;7. DEPARTMENT OF COMBINATORICS & OPTIMIZATION, UNIVERSITY OF WATERLOO, WATERLOO, CANADA;8. INSTITUTE OF MATHEMATICS, SLOVAK ACADEMY OF SCIENCES, BRATISLAVA, SLOVAK REPUBLIC
Abstract:We present two main results: a 2‐page and a rectilinear drawing of the n‐dimensional cube urn:x-wiley:03649024:media:jgt21910:jgt21910-math-0001. Both drawings have the same number urn:x-wiley:03649024:media:jgt21910:jgt21910-math-0002 of crossings, even though they are given by different constructions. The first improves the current best general 2‐page drawing, while the second is the first nontrivial rectilinear drawing of urn:x-wiley:03649024:media:jgt21910:jgt21910-math-0003.
Keywords:2‐page crossing number  rectilinear crossing number  n‐cube  topological graph theory
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