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A Note on α-Drawable k-Trees

David Bremner 1 Jonathan Lenchner 2 Giuseppe Liotta 3 Christophe Paul 4 Marc Pouget 5 Svetlana Stolpner Stephen Wismath 6 
4 ALGCO - Algorithmes, Graphes et Combinatoire
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
5 VEGAS - Effective Geometric Algorithms for Surfaces and Visibility
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : We study the problem of realizing a given graph as an $\alpha$-complex of a set of points in the plane. We study the realizability problem for trees and $2$-trees. In the case of $2$-trees, we confine our attention to the realizability of graphs as the $\alpha$-complex minus faces of dimension two; in other words, realizability of the graph in terms of the $1$-skeleton of the $\alpha$-complex of the point set. We obtain both positive (realizability) and negative (non-realizability) results.
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https://hal-lirmm.ccsd.cnrs.fr/lirmm-00324589
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  • HAL Id : lirmm-00324589, version 1

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David Bremner, Jonathan Lenchner, Giuseppe Liotta, Christophe Paul, Marc Pouget, et al.. A Note on α-Drawable k-Trees. CCCG 2008 - 20th Annual Canadian Conference on Computational Geometry, Aug 2008, Montréal, Québec, Canada. pp.23-26. ⟨lirmm-00324589⟩

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