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Conference Papers Year : 2008

## A Note on α-Drawable k-Trees

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David Bremner
• Function : Author
Jonathan Lenchner
• Function : Author
Giuseppe Liotta
• Function : Author
Christophe Paul
Marc Pouget
Svetlana Stolpner
• Function : Author
Stephen Wismath
• Function : Author

#### 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.

#### Domains

Computer Science [cs] Discrete Mathematics [cs.DM]

### Dates and versions

lirmm-00324589 , version 1 (07-09-2022)

### Identifiers

• HAL Id : lirmm-00324589 , version 1

### Cite

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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