The unavoidable arrangements of pseudocircles

Carolina Medina , Jorge Luis Ramírez Alfonsín (1) , Gelasio Salazar (2)

1 IMAG - Institut Montpelliérain Alexander Grothendieck
2 Department of Combinatorics and Optimization

A fact closely related to the classical Erdos-Szekeres theorem is that cyclic arrangements are the only unavoidable simple arrangements of pseudolines: for each fixed m ≥ 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.

Domaines: Mathématiques [math]

Carolina Medina, Jorge Luis Ramírez Alfonsín, Gelasio Salazar. The unavoidable arrangements of pseudocircles. Proceedings of the American Mathematical Society, In press, ⟨10.1090/proc/14498⟩. ⟨hal-02049473⟩