Crossing numbers and parameterized complexity

Authors:
Michael J. Pelsmajer;Marcus Schaefer;Daniel Štefankovič
Affiliations:
Illinois Institute of Technology, Chicago, IL;DePaul University, Chicago, IL;University of Rochester, Rochester, NY
Venue:
GD'07 Proceedings of the 15th international conference on Graph drawing
Year:
2007

Citing 6
Cited 2

String graphs requiring exponential representations

Journal of Combinatorial Theory Series B
Which crossing number is it anyway?

Journal of Combinatorial Theory Series B
Computing crossing numbers in quadratic time

STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Decidability of string graphs

STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Computing crossing number in linear time

Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Odd crossing number is not crossing number

GD'05 Proceedings of the 13th international conference on Graph Drawing

Removing Independently Even Crossings

SIAM Journal on Discrete Mathematics
Removing independently even crossings

GD'09 Proceedings of the 17th international conference on Graph Drawing

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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 that uses at most 9k crossings, 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.