Geodesic
Arrangements of orthogonal circles with many intersections
Journal of Graph Algorithms and Applications, Special issue on Selected papers from the Twenty-nineth International Symposium on Graph Drawing and Network Visualization, GD 2021 , Tome 27 (2023) no. 2, pp. 49-70.

Voir la notice de l'article provenant de la source Journal of Graph Algorythms and Applications website

An arrangement of circles in which circles intersect only in angles of $\pi/2$ is called an arrangement of orthogonal circles. 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 $(3 + \frac{5}{9})n-O\left(\sqrt{n}\right)$. 
@article{JGAA_2023_27_2_a1,
     author = {Sarah Carmesin and Andr\'e Schulz},
     title = {Arrangements of orthogonal circles with many intersections},
     journal = {Journal of Graph Algorithms and Applications},
     pages = {49--70},
     publisher = {mathdoc},
     volume = {27},
     number = {2},
     year = {2023},
     doi = {10.7155/jgaa.00614},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.7155/jgaa.00614/}
}
TY  - JOUR
AU  - Sarah Carmesin
AU  - André Schulz
TI  - Arrangements of orthogonal circles with many intersections
JO  - Journal of Graph Algorithms and Applications
PY  - 2023
SP  - 49
EP  - 70
VL  - 27
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.7155/jgaa.00614/
DO  - 10.7155/jgaa.00614
LA  - en
ID  - JGAA_2023_27_2_a1
ER  - 
%0 Journal Article
%A Sarah Carmesin
%A André Schulz
%T Arrangements of orthogonal circles with many intersections
%J Journal of Graph Algorithms and Applications
%D 2023
%P 49-70
%V 27
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.7155/jgaa.00614/
%R 10.7155/jgaa.00614
%G en
%F JGAA_2023_27_2_a1
Sarah Carmesin; André Schulz. Arrangements of orthogonal circles with many intersections. Journal of Graph Algorithms and Applications, 
							Special issue on Selected papers from the Twenty-nineth International Symposium on Graph Drawing and Network Visualization, GD 2021
					, Tome 27 (2023) no. 2, pp. 49-70. doi : 10.7155/jgaa.00614. http://geodesic.mathdoc.fr/articles/10.7155/jgaa.00614/

Cité par Sources :