Compatible spanning trees

Authors:
Alfredo García;Clemens Huemer;Ferran Hurtado;Javier Tejel
Affiliations:
Departamento de Métodos Estadísticos, IUMA, Universidad de Zaragoza, Zaragoza, Spain;Departament de Matemítica Aplicada IV, Universitat Politècnica de Catalunya, Barcelona, Spain;Departament de Matemítica Aplicada II, Universitat Politècnica de Catalunya, Barcelona, Spain;Departamento de Métodos Estadísticos, IUMA, Universidad de Zaragoza, Zaragoza, Spain
Venue:
Computational Geometry: Theory and Applications
Year:
2014

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Abstract

Two plane geometric graphs are said to be compatible when their union is a plane geometric graph. Let S be a set of n points in the Euclidean plane in general position and let T be any given plane geometric spanning tree of S. In this work, we study the problem of finding a second plane geometric tree T^' spanning S, such that T^' is compatible with T and shares the minimum number of edges with T. We prove that there is always a compatible plane geometric tree T^' having at most (n-3)/4 edges in common with T, and that for some plane geometric trees T, any plane tree T^' spanning S, compatible with T, has at least (n-2)/5 edges in common with T.