Cell-paths in mono- and bichromatic line arrangements in the plane

Combinatorics We prove that the dual graph of any arrangement of n lines in general position always contains a path of length at least n2/4. Further, we show that in every arrangement of n red and blue lines — in general position and not all of the same color — there is a simple path through at leas...

Ausführliche Beschreibung

Gespeichert in:

Bibliographische Detailangaben
Veröffentlicht in:	Discrete mathematics and theoretical computer science 2014-12, Vol.16 no. 3 (Combinatorics), p.317-322
Hauptverfasser:	Aichholzer, Oswin, Cardinal, Jean, Hackl, Thomas, Hurtado, Ferran, Korman, Matias, Pilz, Alexander, Silveira, Rodrigo I., Uehara, Ryuhei, Valtr, Pavel, Vogtenhuber, Birgit, Welzl, Emo
Format:	Artikel
Sprache:	eng
Schlagworte:	[info.info-dm] computer science [cs]/discrete mathematics [cs.dm] Computer Science discrete geometry Discrete Mathematics Geometry Graphs hamiltonicity line arrangement planar graphs
Online-Zugang:	Volltext
Tags:	Tag hinzufügen Keine Tags, Fügen Sie den ersten Tag hinzu!

Beschreibung
Zusammenfassung:	Combinatorics We prove that the dual graph of any arrangement of n lines in general position always contains a path of length at least n2/4. Further, we show that in every arrangement of n red and blue lines — in general position and not all of the same color — there is a simple path through at least n cells where red and blue lines are crossed alternatingly.
ISSN:	1365-8050 1462-7264 1365-8050
DOI:	10.46298/dmtcs.2088