Pach, János and Toth, Geza (2019) Many touchings force many crossings. JOURNAL OF COMBINATORIAL THEORY SERIES B, 137. pp. 104-111. ISSN 0095-8956
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Abstract
Given n continuous open curves in the plane, we say that a pair is touching if they have finitely many interior points in common and at these points the first curve does not get from one side of the second curve to its other side. Otherwise, if the two curves intersect, they are said to form a crossing pair. Let t and c denote the number of touching pairs and crossing pairs, respectively. We prove that c >= 1/0(5) t(2)/n(2), provided that t >= 10n. Apart from the values of the constants, this result is best possible. (C) 2018 Elsevier Inc. All rights reserved.
Item Type: | Article |
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Uncontrolled Keywords: | Touching; Planar curve; |
Subjects: | Q Science / természettudomány > QA Mathematics / matematika |
SWORD Depositor: | MTMT SWORD |
Depositing User: | MTMT SWORD |
Date Deposited: | 19 Oct 2019 04:31 |
Last Modified: | 17 Apr 2023 14:46 |
URI: | http://real.mtak.hu/id/eprint/102413 |
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