Luis Barba ; Ruy Fabila-Monroy ; Dolores Lara ; Jesús Leaños ; Cynthia Rodrıguez et al. - The Erdős-Sós conjecture for geometric graphs

dmtcs:628 - Discrete Mathematics & Theoretical Computer Science, February 28, 2013, Vol. 15 no. 1 -
The Erdős-Sós conjecture for geometric graphsArticle

Authors: Luis Barba 1; Ruy Fabila-Monroy 2; Dolores Lara 3; Jesús Leaños 4; Cynthia Rodrıguez ; Gelasio Salazar 5,6; Francisco Zaragoza 7

  • 1 Département d'Informatique
  • 2 Centro de Investigacion y de Estudios Avanzados del Instituto Politécnico Nacional
  • 3 Departament de Matemàtica Aplicada II
  • 4 Unidad Académica de Matemáticas [Mexico]
  • 5 Department of Combinatorics and Optimization
  • 6 Instituto de Fisica [Mexico]
  • 7 Departamento de Sistemas [Azcapotzalco]

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 )n2 / 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.

Volume: Vol. 15 no. 1
Section: Combinatorics
Published on: February 28, 2013
Accepted on: June 9, 2015
Submitted on: July 5, 2012
Keywords: [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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