论文信息 - Radial Points in the Plane

Radial Points in the Plane

A radial point for a finite set P in the plane is a pointq??P with the property that each line connecting q to a point ofP passes through at least one other element of P. We prove a conjecture of Pinchasi, by showing that the number of radial points for a non-collinear n -element set P is O(n). We also present several extensions of this result, generalizing theorems of Beck, Szemeredi and Trotter, and Elekes on the structure of incidences between points and lines.

Micha Sharir | János Pach

[1] József Beck,et al. On the lattice property of the plane and some problems of Dirac, Motzkin and Erdős in combinatorial geometry , 1983, Comb..

[2] Leonidas J. Guibas,et al. Combinatorial complexity bounds for arrangements of curves and spheres , 1990, Discret. Comput. Geom..

[3] László A. Székely,et al. Crossing Numbers and Hard Erdős Problems in Discrete Geometry , 1997, Combinatorics, Probability and Computing.

[4] Endre Szemerédi,et al. Extremal problems in discrete geometry , 1983, Comb..

[5] János Pach,et al. Graphs drawn with few crossings per edge , 1996, GD.

[6] János Pach,et al. Combinatorial Geometry , 2012 .

[7] János Pach,et al. Graphs drawn with few crossings per edge , 1997, Comb..

[8] Csaba D. Tóth,et al. Distinct Distances in the Plane , 2001, Discret. Comput. Geom..

[9] György Elekes. On the structure of large homothetic subsets , 1997, Contemporary Trends in Discrete Mathematics.

[10] L. A. Oa,et al. Crossing Numbers and Hard Erd} os Problems in Discrete Geometry , 1997 .

[11] Endre Szemerédi,et al. A Combinatorial Distinction Between the Euclidean and Projective Planes , 1983, Eur. J. Comb..