The Erdos-Sos Conjecture for Geometric Graphs

被引：0

作者：

Barba, Luis ^{[1
,2
]}

Fabila-Monroy, Ruy ^{[3
]}

Lara, Dolores ^{[4
]}

Leanos, Jesus ^{[5
]}

Rodriguez, Cynthia ^{[6
,7
]}

Salazar, Gelasio ^{[8
]}

Zaragoza, Francisco J. ^{[6
]}

机构：

[1] ULB, FNRS, Boursier FRIA, Dept Informat, Brussels, Belgium

[2] Carleton Univ, Sch Comp Sci, Ottawa, ON K1S 5B6, Canada

[3] CINVESTAV, Dept Matemat, Mexico City, DF, Mexico

[4] Univ Politecn Cataluna, Dept Matemat Aplicada 2, Barcelona, Spain

[5] UAZ Mexico, Unidad Acad Matemat, Mexico City, DF, Mexico

[6] UAM Azcapotzalco, Dept Sistemas, Mexico City, DF, Mexico

[7] Univ Waterloo, Dept Combinator & Optimizat, Waterloo, ON N2L 3G1, Canada

[8] UASLP, Inst Fis, Mexico City, DF, Mexico

来源：

DISCRETE MATHEMATICS AND THEORETICAL COMPUTER SCIENCE | 2013年 / 15卷 / 01期

关键词：

extremal graph theory; geometric graph; spanning tree;

D O I：

暂无

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

Let f (n, k) be the minimum number of edges that must be removed from some complete geometric graph G on n points, so that there exists a tree on k vertices that is no longer a planar subgraph of G. In this paper we show that (1/2) n(2)/k-1 - n/2 <= f (n, k) <= 2 n(n-2)/k/2. For the case when k - n, we show that 2 <= f (n, n) <= 3. For the case when k = n and G is a geometric graph on a set of points in convex position, we completely solve the problem and prove that at least three edges must be removed.

引用

页码：93 / 100

页数：8

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