GD 2005: Graph Drawing pp 386-396

# Odd Crossing Number Is Not Crossing Number

• Michael J. Pelsmajer
• Marcus Schaefer
• Daniel Štefankovič
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3843)

## Abstract

The crossing number of a graph is the minimum number of edge intersections in a plane drawing of a graph, where each intersection is counted separately. If instead we count the number of pairs of edges that intersect an odd number of times, we obtain the odd crossing number. We show that there is a graph for which these two concepts differ, answering a well-known open question on crossing numbers. To derive the result we study drawings of maps (graphs with rotation systems).

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## Authors and Affiliations

• Michael J. Pelsmajer
• 1
• Marcus Schaefer
• 2
• Daniel Štefankovič
• 3
• 4
1. 1.Department of Applied MathematicsIllinois Institute of TechnologyChicago
2. 2.Department of Computer ScienceDePaul UniversityChicago
3. 3.Department of Computer ScienceUniversity of RochesterRochester
4. 4.Department of Computer ScienceComenius UniversityBratislavaSlovakia