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

Oswin Aichholzer 1 Jean Cardinal 2 Thomas Hackl 1 Ferran Hurtado 3 Matias Korman 4, 5, 6 Alexander Pilz 1 Rodrigo I. Silveira 3, 7 Ryuhei Uehara 8 Pavel Valtr 9 Birgit Vogtenhuber 1 Emo Welzl 10
1 TU Graz - Graz University of Technology [Graz]
2 ULB - Université Libre de Bruxelles [Bruxelles]
3 UPC - Universitat Politècnica de Catalunya [Barcelona]
4 NII - National Institute of Informatics
5 JST - Japan Science and Technology Agency
6 IRATO / Kawarabayashi Large Graph Project [Japan]
7 CIDMA - Centro de Investigaçao e Desenvolvimento em Matematica e Aplicaçoes
8 JAIST - Japan Advanced Institute of Science and Technology
9 Charles University [Prague]
10 ETH Zürich - Eidgenössische Technische Hochschule [Zürich]
Abstract : 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.
Keywords : Discrete geometry Line arrangement Planar graphs Hamiltonicity
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Article dans une revue
Discrete Mathematics and Theoretical Computer Science, DMTCS, 2014, Vol. 16 no. 3 (in progress) (3), pp.317--322
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Oswin Aichholzer, Jean Cardinal, Thomas Hackl, Ferran Hurtado, Matias Korman, et al.. Cell-paths in mono- and bichromatic line arrangements in the plane. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2014, Vol. 16 no. 3 (in progress) (3), pp.317--322. 〈hal-01188902〉

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