# Degree constrained tree embedding into points in the plane

Akihisa Tamura, Yoshiko Tamura

Research output: Contribution to journalArticle

14 Citations (Scopus)

### Abstract

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.

Original language English 211-214 4 Information Processing Letters 44 4 https://doi.org/10.1016/0020-0190(92)90087-C Published - 1992 Dec 10 Yes

### Fingerprint

Trees (mathematics)
Polynomials
Polynomial Algorithm
Line segment
Pi
Intersect

### Keywords

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

### ASJC Scopus subject areas

• Computational Theory and Mathematics

### Cite this

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

In: Information Processing Letters, Vol. 44, No. 4, 10.12.1992, p. 211-214.

Research output: Contribution to journalArticle

@article{7be620de9e9245e5a35fbcbf317170e1,
title = "Degree constrained tree embedding into points in the plane",
abstract = "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.",
keywords = "combinatorial problems, degree sequences, Design of algorithms, embeddings, trees",
author = "Akihisa Tamura and Yoshiko Tamura",
year = "1992",
month = "12",
day = "10",
doi = "10.1016/0020-0190(92)90087-C",
language = "English",
volume = "44",
pages = "211--214",
journal = "Information Processing Letters",
issn = "0020-0190",
publisher = "Elsevier",
number = "4",

}

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

AN - SCOPUS:0043160038

VL - 44

SP - 211

EP - 214

JO - Information Processing Letters

JF - Information Processing Letters

SN - 0020-0190

IS - 4

ER -