### 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 |
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Journal | Discrete Mathematics |

DOIs | |

Publication status | Accepted/In press - 2017 Jan 1 |

### Fingerprint

### Keywords

- Geometric graph
- Geometric paths

### ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics

### Cite this

*Discrete Mathematics*. https://doi.org/10.1016/j.disc.2017.10.021

**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.

Research output: Contribution to journal › Article

*Discrete Mathematics*. https://doi.org/10.1016/j.disc.2017.10.021

}

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

AN - SCOPUS:85034567795

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

ER -