3Departament de Matemàtica Aplicada II (Universitat Politècnica de Catalunya (UPC) Edifici Omega, Campus Nord Jordi Girona, 1-3 E-08034 Barcelona Spain - Espagne)
Abstract : 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.
https://hal.inria.fr/hal-00990608
Contributeur : Service Ist Inria Sophia Antipolis-Méditerranée / I3s
<>
Soumis le : mardi 13 mai 2014 - 16:28:54
Dernière modification le : mardi 19 décembre 2017 - 13:16:02
Document(s) archivé(s) le : lundi 10 avril 2017 - 22:30:11
