On the Erdős Problem of Empty Convex Hexagons

نویسندگان

  • Jessica L. Nelson
  • Lisette de Pillis
چکیده

Paul Erdős’s Empty Hexagon Problem asks if there exists a number H(6) such that for all sets of n ≥ H points in general position on the plane six of the points form the vertices of an empty convex hexagon. This problem is open.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Planar Point Sets with a Small Number of Empty Convex Polygons

A subset A of a finite set P of points in the plane is called an empty polygon, if each point of A is a vertex of the convex hull of A and the convex hull of A contains no other points of P . We construct a set of n points in general position in the plane with only ≈ 1.62n empty triangles, ≈ 1.94n empty quadrilaterals, ≈ 1.02n empty pentagons, and ≈ 0.2n empty hexagons.

متن کامل

Empty Convex Hexagons in Planar Point Sets

Erdős asked whether every sufficiently large set of points in general position in the plane contains six points that form a convex hexagon without any points from the set in its interior. Such a configuration is called an empty convex hexagon. In this paper, we answer the question in the affirmative. We show that every set that contains the vertex set of a convex 9-gon also contains an empty co...

متن کامل

On empty pentagons and hexagons in planar point sets

We give improved lower bounds on the minimum number of k-holes (empty convex k-gons) in a set of n points in general position in the plane, for k = 5, 6.

متن کامل

[Empty][colored] k-gons - Recent results on some Erdős-Szekeres type problems

We consider a family of problems which are based on a question posed by Erdős and Szekeres in 1935: “What is the smallest integer g(k) such that any set of g(k) points in the plane contains at least one convex k-gon?” In the mathematical history this has become well known as the “Happy End Problem”. There are several variations of this problem: The k-gons might be required to be empty, that is,...

متن کامل

Modified Convex Data Clustering Algorithm Based on Alternating Direction Method of Multipliers

Knowing the fact that the main weakness of the most standard methods including k-means and hierarchical data clustering is their sensitivity to initialization and trapping to local minima, this paper proposes a modification of convex data clustering  in which there is no need to  be peculiar about how to select initial values. Due to properly converting the task of optimization to an equivalent...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2003