Removing Independently Even Crossings

We show that cr(G) ≤ 2 iocr(G) 2 settling an open problem of Pach and T´oth [4, 1]. Moreover, iocr(G) = cr(G) if iocr(G) ≤ 2. 1 Crossing Numbers Pach and T´oth point out in “Which Crossing Number is It Anyway?” that there have been many different ideas on how to define a notion of crossing number including—using current terminology—the following (see [5, 13]): crossing number: cr(G), the smallest number of crossings in a drawing of G, pair crossing number:1 pcr(G), the smallest number of pairs of edges crossing in a drawing of G, odd crossing number: ocr(G), the smallest number of pairs of edges crossing oddly in a drawing of G. ∗ ded abstract of this paper will appear in the proceedings of Graph Drawing 2009. † Partially supported by NSA Grant H98230-08-1-0043. 1 

• Type: Conference
• Year: 2009
• Where: GD
• Authors: Michael J. Pelsmajer, Marcus Schaefer, Daniel Stefankovic
• Keywords: Computer Graphics, GD 2009, Numbers Pach, Open Problem, Smallest Number