Bounded 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%2F00216224%3A14330%2F22%3A00129305" target="_blank" >RIV/00216224:14330/22:00129305 - isvavai.cz</a>
Alternative codes found
RIV/00216208:11320/22:10473770
Result on the web
<a href="http://dx.doi.org/10.1007/s00493-021-4285-3" target="_blank" >http://dx.doi.org/10.1007/s00493-021-4285-3</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00493-021-4285-3" target="_blank" >10.1007/s00493-021-4285-3</a>
Alternative languages
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 >= 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
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
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)
Result continuities
Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
COMBINATORICA
ISSN
0209-9683
e-ISSN
1439-6912
Volume of the periodical
42
Issue of the periodical within the volume
5
Country of publishing house
US - UNITED STATES
Number of pages
28
Pages from-to
701-728
UT code for WoS article
000780265300003
EID of the result in the Scopus database
2-s2.0-85126208639