Holes in Convex and Simple Drawings

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F24%3A10490810" target="_blank" >RIV/00216208:11320/24:10490810 - isvavai.cz</a>

Result on the web

<a href="https://doi.org/10.4230/LIPIcs.GD.2024.5" target="_blank" >https://doi.org/10.4230/LIPIcs.GD.2024.5</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.4230/LIPIcs.GD.2024.5" target="_blank" >10.4230/LIPIcs.GD.2024.5</a>

Result language

angličtina

Original language name

Holes in Convex and Simple Drawings

Original language description

Gons and holes in point sets have been extensively studied in the literature. For simple drawings of the complete graph a generalization of the Erdős-Szekeres theorem is known and empty triangles have been investigated. We introduce a notion of k-holes for simple drawings and study their existence with respect to the convexity hierarchy. We present a family of simple drawings without 4-holes and prove a generalization of Gerken&apos;s empty hexagon theorem for convex drawings. A crucial intermediate step will be the structural investigation of pseudolinear subdrawings in convex drawings.

Czech name

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Czech description

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Type

D - Article in proceedings

CEP classification

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OECD FORD branch

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

Project

<a href="/en/project/GX23-04949X" target="_blank" >GX23-04949X: Fundamental questions of discrete geometry</a><br>

Continuities

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

Publication year

2024

Confidentiality

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

Article name in the collection

Leibniz International Proceedings in Informatics, LIPIcs

ISBN

978-3-95977-343-0

ISSN

1868-8969

e-ISSN

1868-8969

Number of pages

9

Pages from-to

1-9

Publisher name

Schloss Dagstuhl, Leibniz-Zentrum für Informatik

Place of publication

Wadern

Event location

Technische Universität Wien

Event date

Sep 18, 2024

Type of event by nationality

WRD - Celosvětová akce

UT code for WoS article

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