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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 digon-free 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 278 144 395 435 367 033
+digonfree 2 131 3 012 906
great pseudocircles 1 4 11
The following files provide (the sparse6-encoded primal-dual graphs of) all connected arrangements of up to $n=6$ pseudocircles. For more information on the encoding see this page.

File: pseudocircles/connected/all3.mod2s6 (182 bytes)

File: pseudocircles/connected/all4.mod2s6 (2.28 KB)

File: pseudocircles/connected/all5.mod2s6 (203.00 KB)

File: pseudocircles/connected/all6.mod2s6.zip (120.98 MB)

The following files provide (the sparse6-encoded dual graphs of) all intersecting arrangements of up to $n=6$ pseudocircles. For more information on the encoding see this page.

File: pseudocircles/intersecting/all2.mod1s6 (6 bytes)

File: pseudocircles/intersecting/all3.mod1s6 (24 bytes)

File: pseudocircles/intersecting/all4.mod1s6 (196 bytes)

File: pseudocircles/intersecting/all5.mod1s6 (12.19 KB)

File: pseudocircles/intersecting/all6.mod1s6.zip (5.32 MB)

The database of all intersecting $n=7$ requires about 24 GB of storage and is available upon request. However, we provide all digon-free intersecting arrangements for up to $n=7$ pseudocircles.

File: pseudocircles/intersecting/digonfree/all3_digonfree.mod1s6 (12 bytes)

File: pseudocircles/intersecting/digonfree/all4_digonfree.mod1s6 (49 bytes)

File: pseudocircles/intersecting/digonfree/all5_digonfree.mod1s6 (629 bytes)

File: pseudocircles/intersecting/digonfree/all6_digonfree.mod1s6 (136.64 KB)

File: pseudocircles/intersecting/digonfree/all7_digonfree.mod1s6.zip (194.60 MB)

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Last update: November 15 2017 21:44:12. (c) 2017 Stefan Felsner and Manfred Scheucher