Bounded maximum degree conjecture holds precisely for c-crossing-critical graphs with c<=12
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F19%3A10401459" target="_blank" >RIV/00216208:11320/19:10401459 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.4230/LIPIcs.SoCG.2019.14" target="_blank" >https://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>
Alternative languages
Result language
angličtina
Original language name
Bounded maximum 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 >= 13 and d >= 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 <=12, precisely, that there exists a constant D such that every c-crossing-critical graph with c <=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 <=12.
Czech name
—
Czech description
—
Classification
Type
D - Article in proceedings
CEP classification
—
OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GA17-04611S" target="_blank" >GA17-04611S: Ramsey-like aspects of graph coloring</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Article name in the collection
35th International Symposium on Computational Geometry (SoCG 2019)
ISBN
978-3-95977-104-7
ISSN
1868-8969
e-ISSN
—
Number of pages
15
Pages from-to
1-15
Publisher name
Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik
Place of publication
Dagstuhl, Germany
Event location
Portland, Oregon
Event date
Jun 18, 2019
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
—