The Crossing Number of the Cone of a Graph
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14330%2F18%3A00106879" target="_blank" >RIV/00216224:14330/18:00106879 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1137/17M1115320" target="_blank" >http://dx.doi.org/10.1137/17M1115320</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1137/17M1115320" target="_blank" >10.1137/17M1115320</a>
Alternative languages
Result language
angličtina
Original language name
The Crossing Number of the Cone of a Graph
Original language description
Motivated by a problem asked by Richter and by the long standing Harary{Hill conjecture, we study the relation between the crossing number of a graph G and the crossing number of its cone CG, the graph obtained from G by adding a new vertex adjacent to all the vertices in G. Simple examples show that the di ff erence cr (CG) - cr (G) can be arbitrarily large for any fi xed k = cr (G). In this work, we are interested in fi nding the smallest possible di ff erence; that is, for each nonnegative integer k, fi nd the smallest f (k) for which there exists a graph with crossing number at least k and cone with crossing number f (k). For small values of k, we give exact values of f (k) when the problem is restricted to simple graphs and show that f (k) = k + circle minus(root k) when multiple edges are allowed.
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
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
SIAM Journal on Discrete Mathematics
ISSN
0895-4801
e-ISSN
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Volume of the periodical
32
Issue of the periodical within the volume
3
Country of publishing house
US - UNITED STATES
Number of pages
14
Pages from-to
2080-2093
UT code for WoS article
000450810500026
EID of the result in the Scopus database
2-s2.0-85053860050