Three Edge-Disjoint Plane Spanning Paths in a Point Set

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F24%3A10475894" target="_blank" >RIV/00216208:11320/24:10475894 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1007/978-3-031-49272-3_22" target="_blank" >https://doi.org/10.1007/978-3-031-49272-3_22</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/978-3-031-49272-3_22" target="_blank" >10.1007/978-3-031-49272-3_22</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Three Edge-Disjoint Plane Spanning Paths in a Point Set

Popis výsledku v původním jazyce

We study the following problem: Given a set S of n distinct points in the plane, how many edge-disjoint plane straight-line spanning paths of S can one draw? While each spanning path is crossing-free, the edges of distinct paths may cross each other (i.e., they may intersect at points that are not elements of S). A well-known result is that when the n points are in convex position, such paths always exist, but when the points of S are in general position the only known construction gives rise to two edge-disjoint plane straight-line spanning paths. In this paper, we show that for any set S of at least ten points in the plane, no three of which are collinear, one can draw at least three edge-disjoint plane straight-line spanning paths of S. Our proof is based on a structural theorem on halving lines of point configurations and a strengthening of the theorem about two spanning paths, which we find interesting in its own right: if S has at least six points, and we prescribe any two points on the boundary of its convex hull, then the set contains two edge-disjoint plane spanning paths starting at the prescribed points.

Název v anglickém jazyce

Three Edge-Disjoint Plane Spanning Paths in a Point Set

Popis výsledku anglicky

We study the following problem: Given a set S of n distinct points in the plane, how many edge-disjoint plane straight-line spanning paths of S can one draw? While each spanning path is crossing-free, the edges of distinct paths may cross each other (i.e., they may intersect at points that are not elements of S). A well-known result is that when the n points are in convex position, such paths always exist, but when the points of S are in general position the only known construction gives rise to two edge-disjoint plane straight-line spanning paths. In this paper, we show that for any set S of at least ten points in the plane, no three of which are collinear, one can draw at least three edge-disjoint plane straight-line spanning paths of S. Our proof is based on a structural theorem on halving lines of point configurations and a strengthening of the theorem about two spanning paths, which we find interesting in its own right: if S has at least six points, and we prescribe any two points on the boundary of its convex hull, then the set contains two edge-disjoint plane spanning paths starting at the prescribed points.

Druh

D - Stať ve sborníku

CEP obor

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OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Projekt

<a href="/cs/project/GX23-04949X" target="_blank" >GX23-04949X: Stěžejní otázky diskrétní geometrie</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2024

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název statě ve sborníku

Graph Drawing and Network Visualization - 31st International Symposium, GD 2023, Isola delle Femmine, Palermo, Italy, September 20-22, 2023, Revised Selected Papers, Part I.

ISBN

978-3-031-49271-6

ISSN

—

e-ISSN

—

Počet stran výsledku

16

Strana od-do

323-338

Název nakladatele

Springer

Místo vydání

Cham

Místo konání akce

Palermo, Italie

Datum konání akce

20. 9. 2023

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

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