We show that cr(G) ≤ 2 iocr(G) 2 settling an open problem of Pach and T´oth [4, 1]. Moreover, iocr(G) = cr(G) if iocr(G) ≤ 2. 1 Crossing Numbers Pach and T´oth point out in ...
Michael J. Pelsmajer, Marcus Schaefer, Daniel Stef...
In this paper we investigate how certain results related to the HananiTutte theorem can be extended from the plane to surfaces. We give a simple topological proof that the weak Ha...
Michael J. Pelsmajer, Marcus Schaefer, Daniel Stef...
An edge in a drawing of a graph is called even if it intersects every other edge of the graph an even number of times. Pach and T´oth proved that a graph can always be redrawn so...
Michael J. Pelsmajer, Marcus Schaefer, Daniel Stef...
We show that computing the crossing number and the odd crossing number of a graph with a given rotation system is NP-complete. As a consequence we can show that many of the well-k...
Michael J. Pelsmajer, Marcus Schaefer, Daniel Stef...
Distributed hard real-time systems have become a major component of many advanced technical products. Means to ensure their proper quality are thus of paramount importance. To ens...