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