TY - GEN

T1 - Planar point sets determine many pairwise crossing segments

AU - Pach, János

AU - Rubin, Natan

AU - Tardos, Gábor

N1 - Publisher Copyright:
© 2019 Association for Computing Machinery.

PY - 2019/6/23

Y1 - 2019/6/23

N2 - We show that any set of n points in general position in the plane determines n1−o(1) pairwise crossing segments. The best previously known lower bound, Ω n, was proved more than 25 years ago by Aronov, Erdős, Goddard, Kleitman, Klugerman, Pach, and Schulman. Our proof is fully constructive, and extends to dense geometric graphs.

AB - We show that any set of n points in general position in the plane determines n1−o(1) pairwise crossing segments. The best previously known lower bound, Ω n, was proved more than 25 years ago by Aronov, Erdős, Goddard, Kleitman, Klugerman, Pach, and Schulman. Our proof is fully constructive, and extends to dense geometric graphs.

KW - Avoiding edges

KW - Comparability graphs

KW - Computational geometry

KW - Crossing edges

KW - Extremal combinatorics

KW - Geometric graphs

KW - Intersection graphs

KW - Partial orders

UR - http://www.scopus.com/inward/record.url?scp=85068033615&partnerID=8YFLogxK

U2 - 10.1145/3313276.3316328

DO - 10.1145/3313276.3316328

M3 - Conference contribution

AN - SCOPUS:85068033615

T3 - Proceedings of the Annual ACM Symposium on Theory of Computing

SP - 1158

EP - 1166

BT - STOC 2019 - Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing

A2 - Charikar, Moses

A2 - Cohen, Edith

PB - Association for Computing Machinery

T2 - 51st Annual ACM SIGACT Symposium on Theory of Computing, STOC 2019

Y2 - 23 June 2019 through 26 June 2019

ER -