On the Number of Edges in Geometric Graphs Without Empty Triangles

被引：0
|
作者：
Bautista-Santiago, C. [1 ]
Heredia, M. A. [2 ]
Huemer, C. [3 ]
Ramirez-Vigueras, A. [2 ]
Seara, C. [4 ]
Urrutia, J. [5 ]
机构：
[1] Univ Autonoma Metropolitana, Unidad Azcapotzalco, Mexico City, DF, Mexico
[2] Univ Nacl Autonoma Mexico, Mexico City 04510, DF, Mexico
[3] Univ Politecn Cataluna, Dept Matemat Aplicada 4, Barcelona, Spain
[4] Univ Politecn Cataluna, Dept Matemat Aplicada 2, Barcelona, Spain
[5] Univ Nacl Autonoma Mexico, Inst Matemat, Mexico City 04510, DF, Mexico
来源：
GRAPHS AND COMBINATORICS | 2013年 / 29卷 / 06期
关键词：
Geometric graphs; Empty triangles; Combinatorial geometry; Extremal problem; SETS;
D O I：
10.1007/s00373-012-1220-9
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper we study the extremal type problem arising from the question: What is the maximum number ET(S) of edges that a geometric graph G on a planar point set S can have such that it does not contain empty triangles? We prove: . (n2) - O(n log n) <= ET (n) <= (n2) - (n - 2 + [n/8]).
引用
收藏
页码：1623 / 1631
页数：9
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