A note on two geometric paths with few crossings for points labeled by integers in the plane

Atsuhiro Nakamoto, Yoshiaki Oda, Mamoru Watanabe, Tomoki Yamashita

Research output: Contribution to journalArticlepeer-review

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 languageEnglish
Pages (from-to)1109-1113
Number of pages5
JournalDiscrete Mathematics
Volume341
Issue number4
DOIs
Publication statusPublished - 2018 Apr

Keywords

  • Geometric graph
  • Geometric paths

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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