TY - JOUR
T1 - Degree constrained tree embedding into points in the plane
AU - Tamura, Akihisa
AU - Tamura, Yoshiko
N1 - Funding Information:
Correspondence to: A. Tamura, Department tion Sciences, Tokyo Institute of Technology, okayama, Meguro-ku, Tokyo 152, Japan. * Supported by Grant-in-Aids for Co-operative Research (03832017) of the Ministry of Education, Science and Culture.
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 - Design of algorithms
KW - combinatorial problems
KW - degree sequences
KW - embeddings
KW - trees
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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 -