### The Erdős-Sós Conjecture for Geometric Graphs

*Ruy Fabila-Monroy, Luis Felipe Barba, Dolores Lara, Jesús Leaños, Cynthia Rodríguez, Gelasio Salazar, Francisco Zaragoza*

#### 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
)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.Full Text: PDF PostScript