Assume $\mathcal{F}$ such a family of axises-parallel rectangles, any two of them intersects by a horizontal or vertical line. Prove there exist a pair of line $(v, h)$ vertical and horizontal such that any $R\in\mathcal{F}$ intersects any of $(v,h)$.
Asked
Active
Viewed 42 times
0
-
What is your work on the subject? – Jean Marie Dec 11 '16 at 08:48
-
First I thought that the following arguments works, but I find a counterexample... – 123... Dec 11 '16 at 10:05
-
Let $I=[a_1,b_1]\times [c_1,d_1], J=[a_2, b_2]\times[c_2, d_2]\in\mathcal{F}$ be the ones with the most left right-edge and the most down up-edge respectively. Let $X=b_1$ and $Y= d_2$. I tohought the pair $(X, Y)$ has the desired property... – 123... Dec 11 '16 at 10:06