On the number of tangencies among 1-intersecting x-monotone curves

Eyal Ackerman; Balázs Keszegh

doi:10.1016/j.ejc.2024.103929

On the number of tangencies among 1-intersecting x-monotone curves

Eyal Ackerman
, Balázs Keszegh

Department of Mathematics, Physics and Computer Science (Oranim Campus)

Research output: Contribution to journal › Article › peer-review

Abstract

Let C be a set of curves in the plane such that no three curves in C intersect at a single point and every pair of curves in C intersect at exactly one point which is either a crossing or a touching point. János Pach conjectured that the number of pairs of curves in C that touch each other is O(|C|). We prove this conjecture for x-monotone curves.

Original language	English
Article number	103929
Journal	European Journal of Combinatorics
Volume	118
DOIs	https://doi.org/10.1016/j.ejc.2024.103929
State	Published - May 2024

Bibliographical note

Publisher Copyright:
© 2024 The Author(s)

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics

Access to Document

10.1016/j.ejc.2024.103929

Cite this

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title = "On the number of tangencies among 1-intersecting x-monotone curves",

abstract = "Let C be a set of curves in the plane such that no three curves in C intersect at a single point and every pair of curves in C intersect at exactly one point which is either a crossing or a touching point. J{\'a}nos Pach conjectured that the number of pairs of curves in C that touch each other is O(|C|). We prove this conjecture for x-monotone curves.",

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AB - Let C be a set of curves in the plane such that no three curves in C intersect at a single point and every pair of curves in C intersect at exactly one point which is either a crossing or a touching point. János Pach conjectured that the number of pairs of curves in C that touch each other is O(|C|). We prove this conjecture for x-monotone curves.

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DO - 10.1016/j.ejc.2024.103929

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VL - 118

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On the number of tangencies among 1-intersecting x-monotone curves

Abstract

Bibliographical note

ASJC Scopus subject areas

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