The unavoidable arrangements of pseudocircles
classification
🧮 math.CO
keywords
arrangementsunavoidablecyclicpseudocirclespseudolinessimplearrangementevery
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It is known that cyclic arrangements are the only {\em 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.
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