### 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 |

### Keywords

- Geometric graph
- Geometric paths

### ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics

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## Cite this

Nakamoto, A., Oda, Y., Watanabe, M., & Yamashita, T. (Accepted/In press). A note on two geometric paths with few crossings for points labeled by integers in the plane.

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