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The Erdős-Sós conjecture for geometric graphs
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.
Cited literature [7 references]
https://hal.inria.fr/hal-00990608
Contributor : Service Ist Inria Sophia Antipolis-Méditerranée / I3s <>
Submitted on : Tuesday, May 13, 2014 - 4:28:54 PM
Last modification on : Wednesday, December 16, 2020 - 12:56:08 PM
Long-term archiving on: : Monday, April 10, 2017 - 10:30:11 PM
Contributor : Service Ist Inria Sophia Antipolis-Méditerranée / I3s <>
Submitted on : Tuesday, May 13, 2014 - 4:28:54 PM
Last modification on : Wednesday, December 16, 2020 - 12:56:08 PM
Long-term archiving on: : Monday, April 10, 2017 - 10:30:11 PM
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2196-7736-1-PB.pdf
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