Title: Crossing Numbers and Parameterized Complexity
Published: August 2006
Authors: Michael J. Pelsmajer, Marcus Schaefer, Daniel Štefankovic
Abstract: The odd crossing number of G is the smallest number of pairs of edges that cross an odd number of times in any drawing of G. We show that there always is a drawing realizing the odd crossing number of G whose crossing number is at most 9k+1, where k is the odd crossing number of G. As a consequence of this and a result of Grohe we can show that the odd crossing number is fixed-parameter tractable.
Full Paper: [postscript, pdf]