TY - JOUR
AU - Carmesin, Sarah
AU - Schulz, AndrĂ©
PY - 2023/02/01
Y2 - 2024/06/13
TI - Arrangements of orthogonal circles with many intersections
JF - Journal of Graph Algorithms and Applications
JA - JGAA
VL - 27
IS - 2
SE -
DO - 10.7155/jgaa.00614
UR - https://jgaa.info/index.php/jgaa/article/view/paper614
SP - 49-70
AB - An arrangement of circles in which circles intersect onlyin 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 intersectiongraph 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 ofedges 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 wecan also improve the lower bound for the number of triangles in arrangements of orthogonal circles to $(3 + \frac{5}{9})n-O\left(\sqrt{n}\right)$.
ER -