The Same Upper Bound for Both: The 2‐page and the Rectilinear Crossing Numbers of the  n ‐Cube | Zendy

Faria Luerbio | Zendy; de Figueiredo Celina M. H. | Zendy; Richter R. Bruce | Zendy; Vrt'o Imrich | Zendy

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The Same Upper Bound for Both: The 2‐page and the Rectilinear Crossing Numbers of the n ‐Cube

Author(s) -

Faria Luerbio,

de Figueiredo Celina M. H.,

Richter R. Bruce,

Vrt'o Imrich

Publication year - 2016

Publication title -

journal of graph theory

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.164

H-Index - 54

eISSN - 1097-0118

pISSN - 0364-9024

DOI - 10.1002/jgt.21910

Subject(s) - cube (algebra) , combinatorics , mathematics , upper and lower bounds , crossing number (knot theory) , discrete mathematics , mathematical analysis , cartography , intersection (aeronautics) , geography

We present two main results: a 2‐page and a rectilinear drawing of the n ‐dimensional cube Q n . Both drawings have the same number125 768 4 n − 2 n − 3 3 ( 3 n 2 + 9 + ( − 1 ) n + 12 )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 Q n .

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