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

par Aichholzer, Oswin;Hackl, Thomas;Pilz, Alexander;Vogtenhuber, Birgit;Cardinal, Jean ;Hurtado, Ferran ;Silveira, Rodrigo R.I.;Korman, Matias ;Uehara, Ryuhei;Valtr, Pavel;Welzl, Emo
Référence Discrete mathematics and theoretical computer science, 16, 3, page (317-332)
Publication Publié, 2014

Article révisé par les pairs

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Résumé :

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.