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 |
Keywords
- Geometric graph
- Geometric paths
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
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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