Abstract
We prove that the dual graph of any arrangement of η lines in general position always contains a path of length at least n2/4. Further, we show that in every arrangement of η red and blue lines-in general position and not all of the same color-there is a simple path through at least η cells where red and blue lines are crossed alternatingly.
Original language | English |
---|---|
Pages (from-to) | 317-332 |
Number of pages | 16 |
Journal | Discrete Mathematics and Theoretical Computer Science |
Volume | 16 |
Issue number | 3 |
Publication status | Published - 2014 |
Externally published | Yes |
Keywords
- Discrete geometry
- Hamiltonicity
- Line arrangement
- Planar graphs
ASJC Scopus subject areas
- Theoretical Computer Science
- Computer Science(all)
- Discrete Mathematics and Combinatorics