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%2F16%3A00088630" target="_blank" >RIV/00216224:14330/16:00088630 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/978-3-319-50106-2_33" target="_blank" >http://dx.doi.org/10.1007/978-3-319-50106-2_33</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/978-3-319-50106-2_33" target="_blank" >10.1007/978-3-319-50106-2_33</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 difference cr(CG)-cr(G) can be arbitrarily large for any fixed k=cr(G). In this work, we are interested in finding the smallest possible difference, that is, for each non-negative integer k, find 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+Theta(sqrt(k)) when multiple edges are allowed.
Czech name
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Czech description
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Classification
Type
D - Article in proceedings
CEP classification
IN - Informatics
OECD FORD branch
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Result continuities
Project
<a href="/en/project/GA14-03501S" target="_blank" >GA14-03501S: Parameterized algorithms and kernelization in the context of discrete mathematics and logic</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Article name in the collection
Graph Drawing and Network Visualization - 24th International Symposium, GD 2016
ISBN
9783319501055
ISSN
0302-9743
e-ISSN
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Number of pages
12
Pages from-to
427-438
Publisher name
Springer Verlag
Place of publication
Berlin
Event location
Athens, Greece
Event date
Sep 19, 2016
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
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