Bounded degree conjecture holds precisely for c-crossing-critical graphs with c<=12

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14330%2F19%3A00108275" target="_blank" >RIV/00216224:14330/19:00108275 - isvavai.cz</a>

Result on the web

<a href="http://dx.doi.org/10.4230/LIPIcs.SoCG.2019.14" target="_blank" >http://dx.doi.org/10.4230/LIPIcs.SoCG.2019.14</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.4230/LIPIcs.SoCG.2019.14" target="_blank" >10.4230/LIPIcs.SoCG.2019.14</a>

Result language

angličtina

Original language name

Bounded degree conjecture holds precisely for c-crossing-critical graphs with c<=12

Original language description

We study c-crossing-critical graphs, which are the minimal graphs that require at least c edge-crossings when drawn in the plane. For every fixed pair of integers with c &gt;= 13 and d &gt;= 1, we give first explicit constructions of c-crossing-critical graphs containing a vertex of degree greater than d. We also show that such unbounded degree constructions do not exist for c &lt;=12, precisely, that there exists a constant D such that every c-crossing-critical graph with c &lt;=12 has maximum degree at most D. Hence, the bounded maximum degree conjecture of c-crossing-critical graphs, which was generally disproved in 2010 by Dvorák and Mohar (without an explicit construction), holds true, surprisingly, exactly for the values c &lt;=12.

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/GA17-00837S" target="_blank" >GA17-00837S: Structural properties, parameterized tractability and hardness in combinatorial problems</a><br>

Continuities

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

Publication year

2019

Confidentiality

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

Article name in the collection

35th International Symposium on Computational Geometry, SoCG 2019

ISBN

9783959771047

ISSN

1868-8969

e-ISSN

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Number of pages

15

Pages from-to

„14:1-14:15“

Publisher name

Leibniz International Proceedings in Informatics, LIPIcs

Place of publication

Dagstuhl

Event location

Portland, OR, USA

Event date

Jun 18, 2018

Type of event by nationality

WRD - Celosvětová akce

UT code for WoS article

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