GD 1996: Graph Drawing pp 1-10

# Bipartite embeddings of trees in the plane

• M. Abellanas
• J. García
• G. Hernández
• M. Noy
• P. Ramos
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1190)

## Abstract

Given a tree T on n vertices and a set P of n points in the plane in general position, it is known that T can be straight line embedded in P without crossings. Now imagine the set P is partitioned into two disjoint subsets R and B, and we ask for an embedding of T in P without crossings and with the property that all edges join a point in R (red) and a point in B (blue). In this case we say that T admits a bipartite embedding with respect to the bipartition (R, B). Examples show that the problem in its full generality is not solvable. In view of this fact we consider several embedding problems and study for which bipartitions they can be solved. We present several results that are valid for any bipartition (R, B) in general position, and some other results that hold for particular configurations of points.

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## Authors and Affiliations

• M. Abellanas
• 1
• J. García
• 2
• G. Hernández
• 1
• M. Noy
• 3
• P. Ramos
• 4
3. 3.Dep. de Matemàtica Aplicada IIUniv. Politècnica de CatalunyaBarcelonaSpain