@article{Carmesin_Schulz_2023, title={Arrangements of orthogonal circles with many intersections}, volume={27}, url={https://jgaa.info/index.php/jgaa/article/view/paper614}, DOI={10.7155/jgaa.00614}, abstractNote={An arrangement of circles in which circles intersect only
in angles of $\pi/2$ is called an <i>arrangement of orthogonal circles</i>. We show that in the case that no two circles are nested, the intersection
graph of such an arrangement is planar. The same result holds for arrangement of circles that intersect in an angle of at most $\pi/2$. For the case where circles can be nested we prove that the maximal number of
edges in an intersection graph of an arrangement of orthogonal circles lies in between $4n - O\left(\sqrt{n}\right)$ and $\left(4+\frac{5}{11}\right)n$, for
$n$ being the number of circles. Based on the lower bound we
can also improve the lower bound for the number of triangles in arrangements of orthogonal circles to $(3 + \frac{5}{9})n-O\left(\sqrt{n}\right)$.}, number={2}, journal={Journal of Graph Algorithms and Applications}, author={Carmesin, Sarah and Schulz, André}, year={2023}, month={Feb.}, pages={49–70} }