Abstract
Let S be a set of n points in the plane in general position such that the integers 1,2,...,n are assigned to the points bijectively. Set h be an integer with 1≤h<n(n+1)/2. In this paper we consider the problem of finding two vertex-disjoint simple geometric paths consisting of all points of S such that the sum of labels of the points in one path is equal to h and the paths have as few crossings as possible. We prove that there exists such a pair of paths with at most two crossings between them.
| Original language | English |
|---|---|
| Journal | Discrete Mathematics |
| DOIs | |
| Publication status | Accepted/In press - 2017 Jan 1 |
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Keywords
- Geometric graph
- Geometric paths
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
Cite this
A note on two geometric paths with few crossings for points labeled by integers in the plane. / Nakamoto, Atsuhiro; Oda, Yoshiaki; Watanabe, Mamoru; Yamashita, Tomoki.
In: Discrete Mathematics, 01.01.2017.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - A note on two geometric paths with few crossings for points labeled by integers in the plane
AU - Nakamoto, Atsuhiro
AU - Oda, Yoshiaki
AU - Watanabe, Mamoru
AU - Yamashita, Tomoki
PY - 2017/1/1
Y1 - 2017/1/1
N2 - Let S be a set of n points in the plane in general position such that the integers 1,2,...,n are assigned to the points bijectively. Set h be an integer with 1≤h
AB - Let S be a set of n points in the plane in general position such that the integers 1,2,...,n are assigned to the points bijectively. Set h be an integer with 1≤h
KW - Geometric graph
KW - Geometric paths
UR - http://www.scopus.com/inward/record.url?scp=85034567795&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85034567795&partnerID=8YFLogxK
U2 - 10.1016/j.disc.2017.10.021
DO - 10.1016/j.disc.2017.10.021
M3 - Article
JO - Discrete Mathematics
JF - Discrete Mathematics
SN - 0012-365X
ER -