ABSTRACT
We begin with one of the oldest known crossing number problems; its roots go back to a note by Richard Baltzer from 1885. In that note, Baltzer asked, and partially answered, the following question: what is the largest number of crossings in an n-gon? We generalize this problem by introducing the maximum rectilinear crossing number, max- cr ¯ ( G ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315152394/76a56b35-285a-4240-990f-b454c3e374e6/content/eq838.tif"/> of a graph G as the largest number of crossings in a rectilinear drawing of a graph. Baltzer’s problem then asks for max- cr ¯ ( C n ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315152394/76a56b35-285a-4240-990f-b454c3e374e6/content/eq839.tif"/> .
