### 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 |
---|---|

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 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Computational Theory and Mathematics

### Cite this

*Information Processing Letters*,

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

**Degree constrained tree embedding into points in the plane.** / Tamura, Akihisa; Tamura, Yoshiko.

Research output: Contribution to journal › Article

*Information Processing Letters*, vol. 44, no. 4, pp. 211-214. https://doi.org/10.1016/0020-0190(92)90087-C

}

TY - JOUR

T1 - Degree constrained tree embedding into points in the plane

AU - Tamura, Akihisa

AU - Tamura, Yoshiko

PY - 1992/12/10

Y1 - 1992/12/10

N2 - Given a set N = {p1,...,pn} of n points in general position in the plane, and a positive integral n-vector d = (d1,...,dn) satisfying ∑ni=1di=2n - 2, can we construct a tree on N, such that the degree of point pi is di 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.

AB - Given a set N = {p1,...,pn} of n points in general position in the plane, and a positive integral n-vector d = (d1,...,dn) satisfying ∑ni=1di=2n - 2, can we construct a tree on N, such that the degree of point pi is di 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.

KW - combinatorial problems

KW - degree sequences

KW - Design of algorithms

KW - embeddings

KW - trees

UR - http://www.scopus.com/inward/record.url?scp=0043160038&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0043160038&partnerID=8YFLogxK

U2 - 10.1016/0020-0190(92)90087-C

DO - 10.1016/0020-0190(92)90087-C

M3 - Article

VL - 44

SP - 211

EP - 214

JO - Information Processing Letters

JF - Information Processing Letters

SN - 0020-0190

IS - 4

ER -