> pseudocircles
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By exhaustive computations we
generated the complete database of
all connected arrangements of up to $n=6$ pseudocircles and
all intersecting arrangements of up to $n=7$ pseudocircles.
Our program recursively inserted pseudocircles in all possible ways,
starting with the unique arrangement of two intersecting
pseudocircles.
Given this complete database,
it was then easy to filter certain properties,
like digonfree arrangements and/or cylindrical arrangements.
The following table
(from our paper
Arrangements of Pseudocircles: Circularizability) shows the number of combinatorially different
arrangements.
The files containing the arrangements are listed below the table.
n 
3 
4 
5 
6 
7 
connected 
3 
21 
984 
609 423 
? 
+digonfree 
1 
3 
30 
4 509 
? 
con.+cylindrical 
3 
20 
900 
530 530 
? 
+digonfree 


30 
4 477 
? 

intersecting 
2 
8 
278 
145 058 
447 905 202 
+digonfree 
1 
2 
14 
2 131 
3 012 972 
int.+cylindrical 


278 
144 395 
436 634 633 
+digonfree 



2 131 
3 012 906 

great pseudocircles 


1 
4 
11 
Remark:The term for cylindrical connected arrangements on $n=7$ pseudocircles was corrected on April 02, 2018.
The following files provide
(the sparse6encoded primaldual graphs of)
all connected arrangements of up to $n=6$ pseudocircles.
For more information on the encoding
see
this page.
The following files provide
(the sparse6encoded dual graphs of)
all intersecting arrangements of up to $n=6$ pseudocircles.
For more information on the encoding
see
this page.
The database of all intersecting $n=7$ requires about 24 GB of storage and is available upon request.
However, we provide all digonfree intersecting arrangements for up to $n=7$ pseudocircles.
Go back...Last update: April 24 2018 15:44:56.
(c) 2017 Stefan Felsner and Manfred Scheucher