Convex Polygons in Geometric Triangulations

被引：2

作者：

Dumitrescu, Adrian ^{[1
]}

Toth, Csaba D. ^{[2
,3
]}

机构：

[1] Univ Wisconsin Milwaukee, Dept Comp Sci, Milwaukee, WI 53211 USA

[2] Calif State Univ Northridge, Dept Math, Los Angeles, CA USA

[3] Tufts Univ, Dept Comp Sci, Medford, MA 02155 USA

来源：

COMBINATORICS PROBABILITY & COMPUTING | 2017年 / 26卷 / 05期

关键词：

NUMBER; CYCLES; MATCHINGS; BOUNDS;

D O I：

10.1017/S0963548317000141

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

We show that the maximum number of convex polygons in a triangulation of n points in the plane is O(1.5029(n)). This improves an earlier bound of O(1.6181(n)) established by van Kreveld, Loffler and Pach (2012), and almost matches the current best lower bound of Omega(1.5028(n)) due to the same authors. Given a planar straight-line graph G with n vertices, we also show how to compute efficiently the number of convex polygons in G.

引用

页码：641 / 659

页数：19

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