@inproceedings{9299,
abstract = {We call a multigraph non-homotopic if it can be drawn in the plane in such a way that no two edges connecting the same pair of vertices can be continuously transformed into each other without passing through a vertex, and no loop can be shrunk to its end-vertex in the same way. It is easy to see that a non-homotopic multigraph on n>1 vertices can have arbitrarily many edges. We prove that the number of crossings between the edges of a non-homotopic multigraph with n vertices and m>4n edges is larger than cm2n for some constant c>0 , and that this bound is tight up to a polylogarithmic factor. We also show that the lower bound is not asymptotically sharp as n is fixed and m⟶∞ .},
author = {Pach, János and Tardos, Gábor and Tóth, Géza},
booktitle = {28th International Symposium on Graph Drawing and Network Visualization},
isbn = {9783030687656},
issn = {1611-3349},
location = {Virtual, Online},
pages = {359--371},
publisher = {Springer Nature},
title = {{Crossings between non-homotopic edges}},
doi = {10.1007/978-3-030-68766-3_28},
volume = {12590},
year = {2020},
}