Vertex insertion approximates the crossing number of apex graphs

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14330%2F12%3A00057323" target="_blank" >RIV/00216224:14330/12:00057323 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.ejc.2011.09.009" target="_blank" >http://dx.doi.org/10.1016/j.ejc.2011.09.009</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.ejc.2011.09.009" target="_blank" >10.1016/j.ejc.2011.09.009</a>

Result language
angličtina
Original language name
Vertex insertion approximates the crossing number of apex graphs
Original language description
We show that the crossing number of an apex graph, i.e. a graph $G$ from which only one vertex $v$ has to be removed to make it planar, can be approximated up to a factor of $Delta(G-v)cdot d(v)/2$ by solving the emph{vertex inserting} problem, i.e.inserting a vertex plus incident edges into an optimally chosen planar embedding of a planar graph. Due to a recently developed polynomial algorithm for the latter problem, this establishes the first polynomial fixed-constant approximation algorithm forthe crossing number problem of apex graphs with bounded degree.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
IN - Informatics
OECD FORD branch
—

Project
<a href="/en/project/GEGIG%2F11%2FE023" target="_blank" >GEGIG/11/E023: Graph Drawings and Representations</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2012
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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