A Finite Family of Pseudodiscs Must Include a “Small” Pseudodisc
Rom Pinchasi · SIAM Journal on Discrete Mathematics · 2014
We show that there is an absolute constant $c \leq 156$ such that in every finite family ${\cal F}$ of pseudodiscs in the plane one can find a member $D \in {\cal F}$ such that among all of the pseudodiscs in ${\cal F}$ intersecting $D$ there are at most $c$ pairwise disjoint sets.