| | |
| | |
Stat |
Members: 3643 Articles: 2'488'730 Articles rated: 2609
29 March 2024 |
|
| | | |
|
Article overview
| |
|
Beyond the Richter-Thomassen Conjecture | János Pach
; Natan Rubin
; Gábor Tardos
; | Date: |
30 Apr 2015 | Abstract: | If two closed Jordan curves in the plane have precisely one point in common,
then it is called a {em touching point}. All other intersection points are
called {em crossing points}. The main result of this paper is a Crossing Lemma
for closed curves: In any family of $n$ pairwise intersecting simple closed
curves in the plane, no three of which pass through the same point, the number
of crossing points exceeds the number of touching points by a factor of at
least $Omega((loglog n)^{1/8})$.
As a corollary, we prove the following long-standing conjecture of Richter
and Thomassen: The total number of intersection points between any $n$ pairwise
intersecting simple closed curves in the plane, no three of which pass through
the same point, is at least $(1-o(1))n^2$. | Source: | arXiv, 1504.8250 | Services: | Forum | Review | PDF | Favorites |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
browser claudebot
|
| |
|
|
|
| News, job offers and information for researchers and scientists:
| |