The unavoidable arrangements of pseudocircles
Proceedings of the American Mathematical Society, 2019•ams.org
A fact closely related to the classical Erdős-Szekeres theorem is that cyclic arrangements
are the only unavoidable simple arrangements of pseudolines: for each fixed $ m\ge 1$,
every sufficiently large simple arrangement of pseudolines has a cyclic subarrangement of
size $ m $. In the same spirit, we show that there are three unavoidable arrangements of
pseudocircles. References
are the only unavoidable simple arrangements of pseudolines: for each fixed $ m\ge 1$,
every sufficiently large simple arrangement of pseudolines has a cyclic subarrangement of
size $ m $. In the same spirit, we show that there are three unavoidable arrangements of
pseudocircles. References
Abstract
A fact closely related to the classical Erdős-Szekeres theorem is that cyclic arrangements are the only unavoidable simple arrangements of pseudolines: for each fixed , every sufficiently large simple arrangement of pseudolines has a cyclic subarrangement of size . In the same spirit, we show that there are three unavoidable arrangements of pseudocircles. References
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