Straight line embeddings of rooted star forests in the plane

Straight line embeddings of rooted star forests in the plane

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Article ID: iaor20013543
Country: Netherlands
Volume: 101
Issue: 1/3
Start Page Number: 167
End Page Number: 175
Publication Date: Apr 2000
Journal: Discrete Applied Mathematics
Authors: ,
Abstract:

For every 1≤i≤n, let Ti be a rooted star with root νi is not necessarily its center. Then the union F=T1 ∩ T2 ∩ … ∩ Tn is called a rooted star forest with roots ν12,…,νn. Let P be a set of |F| points in the plane in general position containing n specified points p1, p2,…,pn, where |F| denotes the order of F. Then we show that there exists a bijection φ:V(F)→P such that φ(νi) = pi for all 1 ≤ i ≤ n, φ(x) and φ(y) are joined by a straight-line segment if and only if x and y are joined by an edge of F, and such that no two straight-line segments intersect except at their common end-point.

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