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oai:recercat.cat:2117/860442026-02-09T07:16:49Zcom_2072_1033col_2072_452950

00925njm 22002777a 4500 dc Huemer, Clemens author Mier Vinué, Anna de author 2015-08-01 This paper is a contribution to the problem of counting geometric graphs on point sets. More concretely, we look at the maximum numbers of non-crossing spanning trees and forests. We show that the so-called double chain point configuration of N points has Omega (12.52(N)) non-crossing spanning trees and Omega (13.61(N)) non-crossing forests. This improves the previous lower bounds on the maximum number of non-crossing spanning trees and of non-crossing forests among all sets of N points in general position given by Dumitrescu, Schulz, Sheffer and Toth (2013). Our analysis relies on the tools of analytic combinatorics, which enable us to count certain families of forests on points in convex position, and to estimate their average number of components. A new upper bound of O(22.12(N)) for the number of non-crossing spanning trees of the double chain is also obtained. (C) 2015 Elsevier Ltd. All rights reserved. Postprint (author's final draft) Àrees temàtiques de la UPC::Matemàtiques i estadística Graph theory Grafs, Teoria de Lower bounds on the maximum number of non-crossing acyclic graphs