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Geometric tree graphs of points in convex position


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Opened Access Geometric tree graphs of points in convex position

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Author: Hernando, María del Carmen
Hurtado, Ferrán
Márquez Pérez, Alberto
Mora, Mercé
Noy, Marc
Department: Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII)
Date: 1999
Published in: Discrete Applied Mathematics, 93 (1), 51-66.
Document type: Article
Abstract: Given a set P of points in the plane, the geometric tree graph of P is defined as the graph T(P) whose vertices are non-crossing spanning with straight edges trees of P, and where two trees T1 and T2 are adjacent if T2 = T1 − e + f for some edges e and f. In this paper we concentrate on the geometric tree graph of a set of n points in convex position, denoted by Gn. We prove several results about Gn, among them the existence of Hamiltonian cycles and the fact that they have maximum connectivity.
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DOI: doi:10.1016/S0166-218X(99)00006-2

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