### Abstract

Given a set N = {p_{1},...,p_{n}} of n points in general position in the plane, and a positive integral n-vector d = (d_{1},...,d_{n}) satisfying ∑^{n}_{i=1}d_{i}=2n - 2, can we construct a tree on N, such that the degree of point p_{i} is d_{i} and none of the (n - 1) line segments connecting two points corresponding to endpoints of an edge intersect each other (except possibly at its endpoints)? We give a simple proof of the existence of such a tree in any instance and propose an algorithm polynomial on n for constructing one.

Original language | English |
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Pages (from-to) | 211-214 |

Number of pages | 4 |

Journal | Information Processing Letters |

Volume | 44 |

Issue number | 4 |

DOIs | |

Publication status | Published - 1992 Dec 10 |

Externally published | Yes |

### Keywords

- Design of algorithms
- combinatorial problems
- degree sequences
- embeddings
- trees

### ASJC Scopus subject areas

- Theoretical Computer Science
- Signal Processing
- Information Systems
- Computer Science Applications

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## Cite this

Tamura, A., & Tamura, Y. (1992). Degree constrained tree embedding into points in the plane.

*Information Processing Letters*,*44*(4), 211-214. https://doi.org/10.1016/0020-0190(92)90087-C